Vector a with arrow has a magnitude of 64 units and points due west, while vector b with arrow has the same magnitude and points due south. specify the direction relative to due west.
find the magnitude and direction of a with arrow and b with arrow.

The magnitude is 90.5.

The direction of   is 45° south of west.

The direction of   is 45° north of west.

Let suppose the direction of unit vector as follows:

in the eastern direction

in the northern direction

Given:

Vector A with arrow has a magnitude of 64 units and points due west, while vector B with arrow has the same magnitude and points due south.

Therefore,

And

Formula used:

And the direction is given by:

Now,

The magnitude of :

∴ The magnitude is 90.5.

And,

The direction relative to west is

θ = tan⁻¹ (B/A) = tan⁻¹ (64/64) = tan⁻¹ 1 = 45°  south of west

∴ The direction is 45° south of west.

Again,

The magnitude of :

∴ The magnitude is 90.5.

And,

The direction relative to west is

θ = tan⁻¹ (B/A) = tan⁻¹ (64/64) = tan⁻¹ 1 = 45° north of west.

∴ The direction is 45° north of west.

i'm sorry mate, but i am not seeing any figures. i am unable to solve this for you.