1. Vector components
Resolving Vectors

2. Vector Components
If vectors are not perpendicular, using the sine law and cosine law is not always the easiest way to solve vector problems.
Scale diagrams could be used, but human error makes a large variance in answers.
This is especially true for vector problems involving the sum of more than two vectors.

3. Vector Components
An example of this would be engineers designing supports for a bridge; they need to account for the vector sum of many different force vectors acting at a point of support.
It will be necessary to break each vector into two components; the vertical (or y) component and the horizontal (or x) component.
Any vector can be represented as the vector sum of these two components.

4. Example
A velocity of 35 m/s [25.0o N of E] can be drawn and then the x and y components are added as dotted lines (tip-to-tail):
Calculate the components using trig:
x1 = ____________ y1 = ______________
35 m/s y1 x1
25.0o

5. More examples Resolve the following: a) 5.0 m [20.0o W of N]
b) 3.0 cm [N]
c) 1.5 m/s [50.0o W of S] 

6. Next Level up question
Q has components Qx and Qy. Qx = 3.0 cm [E], Qy points South and |Q| = 5.0 cm. Find Q’s direction and Qy’s magnitude.