when might we use something similar to the example given of the 2D vector.
When using vectors, is there ever a scenario when the origin is not fixed?
Is the directional arrow on top of "r" always in the forward direction?
In reality, there can be numerous forces that can be acting onto an object in three-dimensional space.
How can you predict the trajectory of an object when so many forces (vectors) are acting on one object in all different directions?
If units are so important in physics, why do vectors not have them?
Are there other ways to represent direction mathematically other than coordinates (x,y) and using trigonometric values (x=sintheta)?
I think my wires are just getting crossed, but I am having trouble finding a way to connect dimensions and vectors, how will they combine in the future?
If we want to use Vector for the position of giving a location, like where to meet up could that ever be negative?
In general when we are using vector for real world mapping how could it be negative?
In regards to a graph showing the distance an object travels over time, why is it necessary to use unit vectors? Why isn't it appropriate to have multiple coordinates with a best fit line on the graph to depict the position of the object over the course of time?
I am a little confused about the notations used in 2D vectors. So i and j denote a single unit vector and x and y are called "coordinates" which have units and can be positive and negative. Do x and y then specify the magnitude and give units to i and j then?
I am a little confused about the unit vectors "i" and "j". If "x" and "y" are the coordinates, and we use them to specify the direction of positive or negative value, what is the sole purpose of a unitless "i" and "j" vector?
In the picture depicted under "Coordinates and Directions", is the total distance represented by r the same as the area of the box created by the intersection of the x and y coordinates?
If I rolled a ball down a hill, assuming it rolls straight then stops at a certain point. How would you represent this using a vector?
How do you use terminology for position vectors in specific cases? If you had a line going from the origin to coordinate (4,5) for example, would the vector be defined as 4i +5j (with hats on the i and j)?
Are x and y going to be multiplied by j-hat and i-hat like with the y=mx+b formula for regular lines?

What does Einstein's special relativity represent?
Why is it necessary to have unit vectors when the arrows on the axis lines show the positive or negative directions?
Are vectors going to be the primary way we describe position and movement in space in this course?
Is a position vector just a line or is there more to it?
Will we cover 3 coordinate and 4 coordinate vectors in this class?
What is a unit vector defined as? Does it equal the same distance as if it were a 1 on the regular x,y axis?
That is, if we say r=5i+6j, would we plot that the same way as (5,6) coming from the origin?
Is there a notation for a negative value?
To specify a position, does time count as a coordinate?
In the note at the end of this reading, it describes the situation if you "do not change your coordinate system". What would changing the coordinate system entail?
Is it possible to have negative values for vectors? Can coordinates have different dimensions but be describing the same scenario?
Do the arrows that are written on top of the letter (position vector) point in different directions to represent different positions?
How do vectors work when it goes backwards?
Are the points on the plane always going to start at the origin? Or can they start anywhere on the graph?
I am still a little confused about the actual definition of a vector, based off of your arrow example.
According to the example, the tailfeathers represent the origin, the length of the arrow is the distance from the origin, and the tip is our point of interest. If the vector describes the distance we must travel to get to the point of interest from the origin, shouldn't the origin be fixed? In the case of the arrow, the origin is not fixed. When an arrow is shot, it moves through space, and the distance between the tailfeathers and arrow tip is constant, meaning that the vector is the same quantity regardless of where the point of interest is located. Wouldn't a better example be something like an arrow that is attached to a rope and then shot? The origin would be the point of attachment for the rope to the ground, and the vector would be the distance along the rope and arrow shaft to the tip of the arrow head.
I am confused at the difference between x and y and i hat and j hat.

Do the symbols stay the same even when the vector is negative?
Can a vector have two different magnitudes?
The article states that a position vector remains the same if the coordinate system is rotated around the origin. However if the coordinates are rotated, would the direction of the point in space then not change, thus changing the position vector?
What would a 3D or 4D vector tell us in Biology? Example?
For our purposes, will a vector ever move in the negative direction? a
I don't really understand why the i and j are needed to specify direction in the formula r=xi+yj. Do you just add a + or - sign to the i and j to show direction? But why can't you just put a plus or minus sign in front of x and y?
Since the point is the actual position of the point in space, is the rest of the arrow just explaining how the point got there? As in, does the arrow represent the direction of that point?
When specifying a vector, how do we know when we should use the Pythagorean Theorem/Trig to describe the total distance and the direction or when we should use equations containing unit vectors and coordinates? Are there specific times when one should be used over the other?
Can vectors show other coordinates than the two shown, such as velocity or magnitude with the thickness of the vector? Also, equations with unit vectors to show position and positive direction, are these used in the Eigen Vector math problems where we can manipulate the variables of the biological system this way?
Are the little hats above the i and j in the reading only representative of a distance, or could those little hats be representative of any unit?
What do unit vectors measure, if they do not have a unit?
Why does the position vector remain the same when we choose different scale to measure distances with
What is an example of 3 coordinate graph?
Why do we use vectors to describe the third coordinate instead of using another axis on the coordinate plane, i.e. (x, y, z)
I don't understand the purpose of the unit vectors, since the position vector gives the direction as well. Do the unit vectors simply show how far the position vector goes in each directional axis?
If unit vectors have no units then why are they called unit vectors and what is their purpose?

Is the little hat that is placed over the vector similar to the brackets used previously? Are they interchangeable?
How would the equation given in the reading change if a third coordinate/axis is needed to determine the position vector?
Why are i-hat and j-hat used instead of labelling axes with units?
In the article it says that in the equation r = x*i + y*j, i and j are unit vectors that specify the direction of x and y, and yet they are unitless. Can you please explain what is meant by this? Are i and j essentially just
+/- signs?
What is a real-life example of something that has four coordinates that we can graph, if there is one?
Do i (hat) and j (hat) just specify in which direction the vector is going vertically and horizontally?
If the point on the vector does not have to be specified, how do you know when the vector is supposed to end?
"In the reading it says "sometimes a pair of coordinates is simply written as (x,y) - and this pair of numbers written with parentheses around them is described as a "vector". This is OK only if you are never going to change which coordinate system you use," what is a specific example of an instance that the coordinate system used would change making this not okay to do?
In what instances might we use vectors in biological models?
What is the point of adding in the i hat and j hat into the vector equation?
If we are using a 2D graph, why do we write it as r=xi+yj? If we are given a simple point to plot (x,y), drawing the graph from the origin to that point will show the direction, why not just figure out the vectors
(and the direction) that way?
Is there ever a case where the vector can have a direction but no magnitude?
Would you ever assign units to unit vectors?
How do we write vectors for a path that is not a straight line but rather a twisting and turning path, or a path that changes direction?
Specifically what would be unit vectors in a problem? Say you are given the coordinates in a problem, x and y, but in a word problem how would we know what we should note as a unit vector instead?
How are vectors used in the medical world? They seem relevant but i am just trying to see how the two fields relate. Could vectors be used to figure out where to make surgical incisions?

What kind of problems will we be using vectors in this class?
To clarify the position vector equation, do the x and y symbols represent numbers that we can replace if we were to rewrite the equation?
Is the equation r = xi + yj always used for 2D vectors? if vectors are a way of finding the distance or representing a distance between two points, would that be the same as using the distance formula?
Do the same methods of calculating a vector quantity apply when using 3 or 4 dimensions?
Can the x and y points of a vector be negative?
Will there be a point where we have to use trig to find a vector or can we always rely on the square root of
(x^2 + y^2)?
So are i and j only a positive or negative? Or they do they hold a numerical value as well? How are these variables determined?
Why are vectors unitless?
Why do we not distinguish between the position and the vector that points to the position?
Will dimensional analysis ever be used in calculating coordinates/values in vector mathematics?
Position vectors are clearly essential for determining direction and distance, and can be added or subtracted graphically; can two vectors also be multiplied and if so, in which ways?
I'm still not quite sure the purpose of using i and j hat next to (x,y) coordinates. Can you explain the real purpose of using those two "hats"?
How can we define the origin of a vector? For instance, if I chose my origin on top of a mountain I would yield different results, so how do we know we are not establishing the origin on a biased structure?
Can the variables we use in this system such as "i, j, x, y" also represent different ideas based on the context as we have seen in the previous units?
Can you explain/clairify the vector arrow example?
Are i and j unit vectors always going to be added together or will there be instances where you have to multiple, or subtract them?
If so, why?

A vector gives the general of the direction of some entity or quantity in space but how do we know that said item will stay on the same track throughout its motion?
Then how would you solve the equation r=xi+yj (excuse the lack of symbology) in a real life situation?
How will it be incorporated when we are making estimations during everyday events?
Why were the example unit vectors that were depicted in the reading actually unitless?
How do you "pecify the directions we are talking about by drawing two little arrows of unit length (with NO dimensions or units!)" if you're using unit of length isn't that a dimension?
How can I get more practice with vectors? I remember I wasn't very good at doing problems in math class.
Also, the vectors reading we had just dealt with x and y, are we going to deal with Z in this class?
In what situation would there be 4 or more independent coordinates? Are we mainly going to be using only 2-3 this semester?
Why do spatial coordinates get so much more complicated when a 4th coordinate is added? what do you man when you say change coordinates?
If we are using vectors to denote how far something has moved in a particular direction, do we assume that it has moved in a straight line? Can we interpolate from the vector to determine the position at other times?
If the vector is in a particular direction for a "PARTICULAR" distance then, why does it stay the same if the scale to measure distances is changed? For example, if the distance is changed from length to meters, won't you convert the position of the vector to a different spot on the graph?
How exactly does "i" and "j" influence the direction and/or magnitude of the vector?
Based on the direction that the arrow is going relative to the point of origin, can a vector have a negative value or is it absolute value?
When trying to calculate position vectors, will we always use the symbols "i" and "j" to specify direction, even though they only represent positive values? If so, I'll assume negative values are expressed based on the value of the x,y coordinate information?
Is the vector formula just a standard y=mx + b equation? in the vector equation, does "i" and "j" only specify whether the object is moving in a positive or negative direction?
What is the purpose of the x and y coordinates in front of the vectors? Are they magnitudes?

Is it possible to specify the dimensions using angles for a vector in 3D space
If a position vector has a displacement of 0, how do we determine the direction?
Is there ever an instance of having a moving origin? How can an origin be fixed?
Why are unit vectors unitless?
Is it appropriate to write a physical quantity as a scalar when one is only concerned with its magnitude
(i.e. writing 'F' to represent a force without having an arrow on top to indicate it is a vector)?
When using coordinates (x,y) as a vector and keeping our coordinate system the same will we be told that they are a vector and not just coordinates? How would we change the coordinate system if we did know the directions of x and y?
In the reading, it stated that a coordinate pair in parentheses can also represent a vector. How will we know for sure when we're working with vectors if the i-hat and j-hat notations are not shown?
Why are the x and y separated from the i and j, respectively? I thought previously we said that math in science should have units and numbers together? So should x and i be combined into one term instead of split into two?
What operations can you do to vectors? Can you multiply vectors together?
Are vectors describing displacement from the origin in z- direction? Why are vectors necessary when (x.y) can describe a position and direction just as well?
What are some techniques similar to using trigonometry and Pythagorean theorem but that would apply to a 3D coordinate system?
Are i hat and j hat indicating the direction that x and y go in? Or are they actual numbers that just don't have any units?
I learned in other classes that vectors represent a magnitude and a direction. Does that still apply in this class?
I dont understand how you can have a vector in one dimentions, dont you need to have at least two points to form a vector?
When we say r=6i+ (-6)j (I am unable to do the proper notations on the computer), are we basically saying that the position we are focusing on in 6 units in the positive x direction from the origin and 6 units in the negative y direction from the origin?

if a unit vector of i is going in the same direction as an X component on the x-axis, is the X component just a multiple of the unit vector i ?
In the reading it said that "we do NOT distinguish between the point at the tip of the vector -- the position -
- and the vector that points to it from the origin." does the point/position of the vector then go on to infinity?
What do you mean by changing the coordinate system you use? For example, do you mean polar as opposed to Cartesian?
For "The "i" and "j" with hats over them" that specify "positive x and y directions" for the vector equation example, will these variables always be positive for every problem?
Can you give us more analogies so that we can better understand vectors? what is the point of using i and j to find the the length of the vector if we just use x and y in the pythagorean theorem
I understand the difference between a unit vector and a position vector, but why are they both needed? In regular math, we would just use a position vector to find the point on a graph and that seemed to work well, so why do we now need a second type of vector? How does it increase understanding of the position of a point?
Since a vector has a physical meaning attached to it, why is a vector signified by an arrow on a graph?
"the displacement from the origin in a particular direction for a particular distance." this seems to mean it has a physical value. an arrow seems to denote that the line is continuous and will keep on going past the value its representing.
When are discussing about by drawing two little arrows of unit length in our two perpendicular directions, what is the purpose of them if they have no dimensions or units? Do they serve as placeholders or indicators of direction?
How are vectors used in the context of biology and how will we have to use them in problems?
The last bullet point under Warning notes states "Sometimes a pair of coordinates is simply written as
(x,y) - and this pair of numbers written with parentheses around them is described as a "vector"." Does this mean the vector's tail is at the origin so that we can figure out the direction using trig?
What does it mean for the unit vector to not have any dimensions? And what exactly does a vector represent, some objects position and its direction? And if a vector does represent a the direction and position of a point, is it possible for one coordinate pair to have multiple vectors, that is, can two vectors have the same position but different directions?

What exactly do the unit vectors have to do with the unit coordinates? Also what do you mean you can rotate the coordinates without changing the vector as long as the origin is fixed?
Is it wrong to think of a vector as a bridge leading from the origin to the desired place?
So vectors are expressed as r = xi + yj, but what does this exactly tell us about the position and direction that the vector is going in? It makes it seem like the i and j are effectively just the point at which the tip is at and that x and y just say whether or not it travels n a negative or positive direction in their respective axis, is that correct? Also when describing a vector is the entire line from the origin to the point counted as a whole to be a vector?
If a vector indicates both direction and position, then doesn't that mean the quantity is moving? And if this is true then is a vector really a representation at a specific time rather than an exact representation? How do you know if past that point in time the direction changes?
I don't understand how unit vectors doing have any units attached with them, please explain
If a pair of coordinates is written as (x,y), should you always assume that the i-hat and j-hat are hidden? If so, would you then assume that the direction of x and y just depends on if they are positive or negative since the i and j-hat have a vector with size 1?
Why are the unit vectors unitless?
When comparing two vectors in terms of force, would the longer of the two have a greater force, or just go for a longer distance?
Since the vector is simply representing a point, why must there be a line from the origin
If one were to rotate the coordinate system around the origin, I understand how its distance would not change from the origin, but how would its position not change either?
For all intents and purposes in our class, how many reference points will we be using. Would it be mainly
2, since it's easier to understand, or 3, in order to make sense of the real world?
Can vectors be added an subtracted? What about multiplied and divided? I would imagine they couldn't be easily multiplied or divided. And what would that mean for a real life situation?
What is an example of a 1D vector in biology? How can anything be 1D?
What are vectors used to actually measure in terms of physics?
Do we use the a2 + b2 = C2 rule when solving for vectors?
Is "r" measuring the total distance between vector Y and the Vector X?

Does the number of coordinates we can successfully use end at 4?
Does i and j mainly specify position direction direction while x and y are numerical distances? Or are they both simply specifying the angle and direction the position director is pointing?
How does multiplying the unit vectors (with no dimensions or units) with a distance (which as units) produce a direction?