Question

Calculate the scalar product of the following vectors.
The vectors a and b make an angle $\phi =2\pi /3.$ Being given that $|a|=3and|b|=4,calculate(3a-2b)(a+2b).$

Answer 1

Given $\cos (a,b)=-\frac{1}{2},|a|=3,|b|=4$

$(3a-2b).(a+2b)=3|a{|}^2-4|b{|}^2+4a.b=3\left(3^2\right)-4\left(4^2\right)+4\left(3\right)\left(4\right)(-\frac{1}{2})$

$(3a-2b).(a+2b)=-61$