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)

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

Answer 2

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 E(i)]
$=0-0=0$