Question

If $a$ is a vector perpendicular to both $b$ and $c$, then

• A. $a\cdot (b\times c)=0$
• B. $a\times (b\times c)=0$
• C. $a\times (b+c)=0$
• D. $a+(b+c)=0$

Answer 1

Answer: (B)

Given, $a$ is perpendicular to both $b$ and $c$.
Then, $a\cdot b=0\text{ and }a\cdot c=0...(i)$
Now, we have
$a\times (b\times c)=(a\cdot c)b-(a\cdot b)c$
$=(0)b-(0)c$ [from Eq.(i)]
$=0-0=0$