Vector upper a overscript right-arrow endscripts has a magnitude of 69 units and points due west, while vector upper b overscript right-arrow endscripts has the same magnitude and points due south. find the magnitude and direction of (a) upper a overscript right-arrow endscripts plus upper b overscript right-arrow endscripts and (b) upper a overscript right-arrow endscripts minus upper b overscript right-arrow endscripts. specify the directions relative to due west.

Refer to the figure below.

Define unit vectors as follows:
in the eastern direction
in the northern direction

Given:
Vectors a and b point due west and south respectively. Therefore


Part (a)

The magnitude is
|-69(√[1² + 1²])| = 69√2 = 97.58.
The direction relative to west is
θ = tan⁻¹ (b/a) = tan⁻¹ 1 = 45°  south of west

The magnitude of (a + b) is 97.58 or 69√2.
The direction is 45° south of west.

Part (b).

The magnitude is
|69(√(1+1)| = 69√2 = 97.58.
The direction relative to west is
tan⁻¹ (b/a) = 45° north of west.

The magnitude of (a-b) is 97.58 or 69√2.
The direction is 45° north of west.