The angle between vector and the resultant of and and is

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Solution

Q.
The angle between vector $\vec{Q}$ and the resultant of $(2 \vec{Q} + 2 \vec{P})$ and $(2 \vec{Q} - 2 \vec{P})$ and is [2024]

1 $\tan^{- 1} (\frac{2 Q}{P})$

2 $\tan^{- 1} (\frac{P}{Q})$

3 $0^{o}$

4 $\tan^{- 1} (\frac{2 \vec{Q} - 2 \vec{P}}{2 \vec{Q} + 2 \vec{P}})$

Ans.
(3)

Resultant $\vec{R} = (2 \vec{Q} + 2 \vec{P}) + (2 \vec{Q} - 2 \vec{P})$

$\vec{R} = 4 \vec{Q}$

Angle between $\vec{Q}$ and $\vec{R}$ is zero.

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