Please explain in words how would you do this, no solution needed -
The vectors a and b have lengths 5 and 3, respectively. The vectors a+2b and 2a-3b are perpendicular. Determine the angle between a and b.
(a+2b)•(2a-3b) = 0
2a•a + 4a•b - 3a•b - 6b•b = 0
Now, you know v•v = |v|^2
and u•v = |u| |v| cosθ
see what you can do with that.