If | a|=5, | b|=4, | c|=3, what will be the value of a b+ b c+ c a, given that a+ b+ c= 0?

Question

If $|\vec a|=5$, $|\vec b|=4$, $|\vec c|=3$, what will be the value of $\vec a\cdot\vec b+\vec b\cdot\vec c+\vec c\cdot\vec a$, given that $\vec a+\vec b+\vec c=\vec 0$?

Accepted Answer

$$|\vec a+\vec b+\vec c|^2=0 \implies 25+16+9+2(\vec a\cdot\vec b+\vec b\cdot\vec c+\vec c\cdot\vec a)=0$$

$$\vec a\cdot\vec b+\vec b\cdot\vec c+\vec c\cdot\vec a = \frac{-50}2=-25$$

Solutions · 1