Vector A has a magnitude of

Question

12.3 units and points due west. Vector B points due north. (a) What
is the magnitude of B if A + B has a magnitude of 15.0 units? (b)
What is the direction of A + B relative to due west? (c) What is the
magnitude of B if A - B has a magnitude of 15.0 units? (d) What is
the direction of A - B relative to due west?

Answer 1

The two vectors are at 90°, so the magnitude of the sum is given by √(A^sup2;+B²).

(a)
√(12.3²+B²)=15
solve for B.
(b)
Angle relative to west, θ
tan(θ)=|B|/12.3
Solve for θ
(c)
A-B = A + (-B)
So (c) and (d) can be solved the same way as (a) and (b), but with the direction of B reversed (due south).