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Question: Answered & Verified by Expert
If $a$ is vector perpendicular to both $b$ and $c$, then
MathematicsVector AlgebraCOMEDKCOMEDK 2016
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:
2809 Upvotes Verified Answer
The correct answer is: $a \times(b \times c)=0$
Given, $a$ is perpendicular to $b$ and $c$. Thus, $\mathbf{a}$ is perpendicular to the plane of $\mathbf{b}$ and $\mathbf{c}$. Now, cross product of $b$ and $c$ will give a vector perpendicular to plane of $b$ and $\boldsymbol{c}$. This vector will be parallel to a.
Now, cross product of two parallel is zero vector.
Thus, $\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=0$

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