# Compute the angle between two vectors if two equations are known

I need to solve the following problem. Which approach should I use ? Is there any simple procedure for such problem ?

Determine the angle between vectors $\vec{a}$ and $\vec{b}$ if:
$(\vec{a} + 3\vec{b}) \perp (7\vec{a} - 5\vec{b})$
and
$(\vec{a} - 4\vec{b}) \perp (7\vec{a} - 2\vec{b})$

• @almagest I don't follow. Would you expand your answer to clarify how you get $a^2=b^2$? – Tim Thayer Sep 26 '15 at 21:21