Motion in a Plane - Result Question 5
5. Vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are such that $\vec{A} \cdot \vec{B}=0$ and $\vec{A} \cdot \vec{C}=0$. Then the vector parallel to $\vec{A}$ is
[NEET Kar. 2013]
(a) $\vec{B}$ and $\vec{C}$
(b) $\vec{A} \times \vec{B}$
(c) $\vec{B}+\vec{C}$
(d) $\vec{B} \times \vec{C}$
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Solution:
- (d) Vector triple product
$\vec{A} \times(\vec{B} \times \vec{C})=\vec{B}(\vec{A} \cdot \vec{C})-\vec{C}(\vec{A} \cdot \vec{B})=0$
$\Rightarrow \vec{A} |(\vec{B} \times \vec{C})$
(c) Using the law of vector addition, $(\vec{d}+\vec{e})$ is as shown in the fig.
