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Question: Answered & Verified by Expert
If $\mathbf{a}$ is a vector perpendicular to both $\mathbf{b}$ and $\mathbf{c}$, then
MathematicsVector AlgebraKCETKCET 2013
Options:
  • A $\mathrm{a} \cdot(\mathrm{b} \times \mathrm{c})=0$
  • B $a \times(b \times c)=0$
  • C $a \times(b+c)=0$
  • D $a+(b+c)=0$
Solution:
2229 Upvotes 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)]
$=0-0=0$

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