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:

  1. (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.

$\therefore \vec{d}+\vec{e}=\vec{f}$