# Calculus - Determining values of perpendicular vectors

The vectors a and b are unit vectors that make an angle of 60 degrees with each other. If a-3b and ma+3b are perpendicular, determine the value of m. I'm lost and am not sure on how to begin solving this question.

• Try computing the dot product $$(a - 3b) \cdot (ma + 3b)$$. – user61527 May 22 '14 at 2:45
• I did and I got: ma^2 - ab + 3mab - 3b^2. I am not sure what follows this though – user481710 May 22 '14 at 2:49

$\left \langle a,b \right \rangle$ = $\left \| a \right \|$.$\left \| b \right \|$.cos(60) but a and b are unit vectors so $\left \langle a,b \right \rangle$ = cos(60). $\left \langle a-3b,ma+3b \right \rangle$ = 0 because cos(90) = 0. You should be able to conclude the rest.