Question

Vector A has a magnitude of 12.0 units and points due west. Vector B points due north. (a) Magnitude of B if A+B is 14.4 units? (b) Direction of A+B relative to due west? (c) Magnitude of B if A-B has 14.4 units (d) Direction of A-B rel. to due west?

Answer 1

Here,angle between the given two vectors is `90`,so if `A+B =14.4` we can say, `(A+B)^2 = A^2 +B^2 + 2AB cos 90` ,so`B = 7.95` units.

if direction of `A+B` makes an angle of `theta` w.r.t west i.e vector`A` we can say `tan theta` = `(B/A)` or `theta` = `33.52`

similarly, if`A-B` is `14.4`, `B` will also be `7.95` (refer to equation of vector sum),and it will also make `33.52` degrees w.r.t west