Question

Vector A has a magnitude of 8.00 units and makes an angle of 45.0° with the positive x-axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x-axis. Find (a) the vector sum A + B and (b) the vector sum of A-B?

Answer 1

A + B = 6,123 units at angle 112,5 degrees.
A - B = 14,782 units at angle 22,5 degrees.

Explanation:

For vector addition, we resolve each vector into horizontal and vertical components and then add each direction separately.
The overall magnitude is ten found from Pythagoras, and the direction from a trig ratio. (Details in sketch)

For vector subtraction, simply add the negative of the second vector and repeat the process.