Question

If $a$ , $b$ and $c$ are three non-zero vectors such that $a.|b\times c|=0$ and $b$ and $c$ are not parallel then $a$ , $b$ and $c$ are

• A. Collinear
• B. Coplanar
• C. May be both
• D. None

Answer 1

Answer: (B)

Coplanar

Given $a,b,c$ are three non zero vectors , $b$ and $c$ are not parallel

Given $a.(b\times c)=0$

So the angle between $a$ and $b\times c$ is ${90}^0$ , which implies they are perpendicular

$b\times c$ is perpendicular to the plane of $b$ and $c$

Therefore $a,b,c$ lies in same plane , so they are coplanar

Therefore the correct option is $B$