SATHEE: Motion in a Plane - Result Question 5

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.

$∴ \vec{d} + \vec{e} = \vec{f}$

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Motion in a Plane - Result Question 5

5. Vectors A→,B→ and C→ are such that A→⋅B→=0 and A→⋅C→=0. Then the vector parallel to A→ is

Solution:

∴d→+e→=f→

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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

$∴ \vec{d} + \vec{e} = \vec{f}$