Question

Calculate the scalar product of the following vectors.
Being given that $|a|=2,|b|=5,and\stackrel{}{(a,b)}=2\pi /3,$ find the value of $\alpha$ for which the vectors $p=\alpha a+17bandq=3a-b$ are perpendicular.

Answer 1

If p and q are two mutually perpendicular then $p.q=0$

$p.q=(\alpha a+17b).(3a-b)=3\alpha |a{|}^2-17|b{|}^2+(51-\alpha )|a||b|\cos (a,b)=0$

$12\alpha -425+(51-\alpha )10\times (-\frac{1}{2})=0$

$17\alpha -680=0$

$\alpha =\frac{680}{17}=40$