Question

Let $u,v$ and $w$ be vectors such that $u+v+w=0$. If $|u|=3,|v|=4$ and $|w|=5$, then $u.v+v.w+w.u$ is equal to

• A. $0$
• B. $-25$
• C. $25$
• D. $50$
• E. $47$

Answer 1

The correct option is B $-25$

Given, $|u|=3,|v|=4$ and $|w|=5$

Also, $u+v+w=0$

On squaring both sides, we get

$|u{|}^2+|v{|}^2+|w{|}^2+2(u.v+v.w+w.u)=0$

$\Rightarrow 3^2+4^2+5^2+2(u.v+v.w+w.u)=0$

$\Rightarrow 9+16+25+2(u.v+v.w+w.u)=0$

$\Rightarrow u.v+v.w+w.u=-\frac{50}{2}=-25$