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If $\mathbf{a}$ is a vector perpendicular to both $\mathbf{b}$ and $\mathbf{c}$, then
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Verified Answer
The correct answer is:
$a \times(b \times c)=0$
Given, $a$ is perpendicular to both $b$ and c.
Then, $\quad a \cdot b=0$ 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)]
$=0-0=0$
Then, $\quad a \cdot b=0$ 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)]
$=0-0=0$
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