Question

If $a$ is perpendicular to $b$ and $c$ then

• A. $a\times (b\times c)=1$
• B. $a\times (b\times c)=0$
• C. $a\times (b\times c)=-1$
• D. None of these

Answer 1

The correct option is B $a\times (b\times c)=0$

Given, $a$ is perpendicular to $b$ and $c.$

Thus, $a$ is perpendicular to the plane of $b$ and $c.$

Now, cross product of $b$ and $c$ will give a vector perpendicular to plane of $b$ and $c.$

This vector will be parallel to $a.$

Now, cross product of two parallel is zero vector.

Thus,

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