physics
posted by raghavendra .
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

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.