Question

If $a.(b\times c)=0$, then which of the following statements can be true:

• A. out of $a,b,c$ any two vectors are parallel
• B. $a,b,c$ are coplanar
• C. any two are equal
  
• D. $a,b,c$ are perpendicular

Answer 1

Answer: (A), (B), (C)

any two are equal
out of $a,b,c$ any two vectors are parallel
$a,b,c$ are coplanar

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

$\Rightarrow$ Scalar triple product of the three vectors is zero.

$\Rightarrow$ Either $a,b$ and $c$ are coplanar or out of $a,b,c$ any two vectors are parallel

Also if any two vectors among $a,b$ and $c$ are equal, the scalar triple product is zero.