Question

For the non - zero vectors $a,b$and $c$ the relation$a.\left(b\times c\right)=0$ is true, if?

• A. $b\perp c$
• B. $a\perp b$
• C. $a\left|\right|c$
• D. $a\perp c$

Answer 1

The correct option is C

$a\left|\right|c$

Step 1: Given data

$a,b,c$are non-zero vectors

For non-zero vectors, we know that

$a.\left(b\times c\right)=0$

Step 2: To find $a.\left(b\times c\right)=0$ is true

If $a\parallel c\Rightarrow a=kc$where $k$ is any constant

Then $$\begin{gathered} \left[abc\right]=\left[kcbc\right] \\ =k\left[cbc\right] \\ =k.0 \\ =0 \end{gathered}$$

Hence when $a\parallel c$ , $a.\left(b\times c\right)=0$ is true

Therefore Option C is the correct answer.