Vector and Vector Resolution
Scalar
Vector
Vectors
Vector Addition
• VECTOR ADDITION – If 2 similar vectors
point in the SAME direction, add them.
• Example: A man walks 54.5 meters east,
then another 30 meters east. Calculate his
displacement relative to where he started.
Vector Subtraction
• VECTOR SUBTRACTION - If 2 vectors are
going in opposite directions, you SUBTRACT.
• Example: A man walks 54.5 meters east, then
30 meters west. Calculate his displacement
relative to where he started.
More Examples
Vectors Are Typically Drawn to Scale
So How Do We Add These?
Pythagorean Theorem
Example
Resultant and Components
 Resultant - The “result” from adding or
subtracting vectors.
 Components- The legs of the triangle or the parts
that make up the resultant.
Adding Vectors that are at different
angles
 Head to Tail Method – easiest method to use to
add vectors; always add vectors “head to tail”
 Parallelogram Method- another way to add
vectors
 Graphical Method- another way to add vectors;
involves drawing to scale and measuring
Example
• Eric leaves the base camp and hikes 11 km,
north and then hikes 11 km east.
Determine Eric's resulting displacement.
PARALLELOGRAM METHOD
Graphical Method
The order does not matter!
 Same three vectors added in a
different order.
 Same resultant
Animation
Resultants
Tail Wind
Head Wind
Cross Wind
To calculate velocity
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(100 km/hr)2 + (25 km/hr)2 = R2
10000 km2/hr2 + 625 km2/hr2 = R2
10625 km2/hr2 = R2
SQRT(10 625 km2/hr2) = R
103.1 km/hr = R
Vectors include direction!
 Therefore anytime we are dealing with a direction we must
give direction. If it is not due north, south, east, or west, an
angle must also be given.
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tan q= (opposite/adjacent)
tan q= (25/100)
q = inverse tan (25/100)
q = 14.0 degrees
Direction should be given from one of
the cardinal directions on the earth.
Animation
Example
• A boat moves with a velocity of 15 m/s, N
in a river which flows with a velocity of 8.0
m/s, west. Calculate the boat's resultant
velocity with respect to due north.
Sometimes we need to find the
components of a vector
 Vector resolution is the process of breaking down
one vector into its parts called components.
 Components are two vectors added together which
give the resultant.
 When asked or necessary, you will need to find the
values of both components.
 These are generally given from a cardinal direction
on the earth (N,S, E, W) or horizontal or vertical.
Example
• A plane moves with a velocity of 63.5 m/s
at 32 degrees South of East. Calculate the
plane's horizontal and vertical velocity
components.