Vectors PowerPoint Notes
- Geometric
Vectors have both _____________________ and ________________________.
Magnitude = length. (also called ________________)
Direction is determined by the angle (measured counterclockwise) the line segment makes with the
_________________________________.
Vector addition
– draw so that the tail of the _______________ vector coincides with the ______________ of the
first vector.
Complete the triangle by drawing the ________________________ from the tail of the first vector
to the head of the second vector.
u
v
The magnitude of the resultant is found by: _______________________________________.
Example:
a has an initial point at 1,3  and a terminal point at  4,6 
Placing the tail of b on the head of vector a results in the
terminal point of b being at  9,8  .
The x-component of the resultant
is ____ and the y-component is ____.
So, a+b=________________________________.
VECTORS PP 2
ALGEBRAIC
Unit Vector– a vector with a magnitude of 1: ________________________________.
Sometimes it is helpful to find a unit vector that has the same ______________ as a given nonzero
vector, v. To do this, divide v by its magnitude: u  unit vector  v   1  v .
 v 
v


The vector u is called a ______________________________ in the direction of v.
__________________________ – vector whose initial point is the origin and is uniquely
represented by the coordinates of its terminal point. The coordinates are the components of v.
pq  q1  p1, q2  p2   v1,v 2   v
Component Form of pq =_________________________________
Polar Form -  x , y   _____________________________
Try: Given
point: v1   2, 3 and terminal point: v 2   7, 9 .
 v  initial
___________________________
1st: Determine the unit vector in the same direction:
2nd: Determine the component form:
3rd: Determine the Polar Form:
VECTOR OPERATIONS:
Vector Addition:______________________________________________________________
Scalar Multiplication:__________________________________________________________
Parametric Vector Equations: x  a  tc; y  b  td
Given: RS, R 1, 5  and v   2, 3  , the vector equation is_________________________.
The parametric equations are_____________________________________________________.
Given: P  5, 8 ; Q 11, 2 Find a direction vector and a pair of parametric equations.
Direction Vector:_________________________________________________
Vector Equation:_________________________________________________
Parametric Equations:____________________
_________________________
VECTORS PP 3
MODELING
x  V0 cos   t
An object is launched into the air at an angle q with the ground and with
an initial velocity of
y  V0 sin  t  S0  16t 2
magnitude V0=ft/sec.
Parametric Equations:
A football is thrown from a height of 7 ft at 35° with initial Velocity of 55 ft/sec.
Find the parametric equations that represent the problem situation: ___________ ___________
TWO METHODS FOR PROBLEM SOLVING:
METHOD 1 - __________________________________________________
A plane is flying with a bearing of 65º east of North at 500 mph. There is a tail wind with a bearing
of 35 º east of North at 80 mph. Find the actual velocity (ground speed) of the plane.
Let v = velocity of plane
u = velocity of tailwind
v  u  _________________________________
METHOD 2 - __________________________________________________
v : direction angle = _______; magnitude = _______________
 x , y   _______________________________
u : direction angle = _______; magnitude = _______________
 x , y   _______________________________
v + u = ___________________________________________
v  u  __________________________________________