Question

The magnitude of two vectors p and q differ by 1. The magnitude of their resultant makes an angle of tan inverse ( 3 / 4 ) with p. The angle between p and q is

Answer 1

hmmm...
If θ is the angle between p+q and p, cosθ = 4/5
If Ø is the angle between p+q and q, then the angle between p and q is θ+Ø

Let's let |q| = a, so |p| = a+1

p•q = a(a+1)cos(θ+Ø)
(p+q)•p = |p+q|*|p| cosθ = (4/5)(a+1)|p+q|
(p+q)•q = |p+q|*|q| cosØ = |p+q|(a) cosØ
|p+q| = pcosθ + qcosØ = (4/5)(a+1) + acosØ

Somewhere in those equations you can surely solve for a and Ø, and you want θ+Ø.

Play around with that, while I do the same.

Or, there may be a handy formula I have forgotten.