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If $a$ is vector perpendicular to both $b$ and $c$, then
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Verified Answer
The correct answer is:
$a \times(b \times c)=0$
Given, $a$ is perpendicular to $b$ and $c$. Thus, $\mathbf{a}$ is perpendicular to the plane of $\mathbf{b}$ and $\mathbf{c}$. Now, cross product of $b$ and $c$ will give a vector perpendicular to plane of $b$ and $\boldsymbol{c}$. This vector will be parallel to a.
Now, cross product of two parallel is zero vector.
Thus, $\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=0$
Now, cross product of two parallel is zero vector.
Thus, $\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=0$
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