JEE MAIN - Physics (2024 - 5th April Morning Shift - No. 18)

The angle between vector $$\vec{Q}$$ and the resultant of $$(2 \vec{Q}+2 \vec{P})$$ and $$(2 \vec{Q}-2 \vec{P})$$ is :
$$ \tan ^{-1}(\mathrm{P} / \mathrm{Q}) $$
0$$^\circ$$
$$ \tan ^{-1} \frac{(2 \vec{Q}-2 \vec{P})}{2 \vec{Q}+2 \vec{P}} $$
$$ \tan ^{-1}(2 Q / \mathrm{P}) $$

Explanation

To find the angle between the vector $$\vec{Q}$$ and the resultant of $$(2 \vec{Q}+2 \vec{P})$$ and $$(2 \vec{Q}-2 \vec{P})$$, we first find the resultant vector of $$(2 \vec{Q}+2 \vec{P})$$ and $$(2 \vec{Q}-2 \vec{P})$$.

The resultant vector of $$(2 \vec{Q}+2 \vec{P})$$ and $$(2 \vec{Q}-2 \vec{P})$$ can be simply found by adding these two vectors:

$$ \text{Resultant} = (2 \vec{Q}+2 \vec{P}) + (2 \vec{Q}-2 \vec{P}) = 4 \vec{Q} $$

Now, we need to find the angle between the vector $$\vec{Q}$$ and this resultant vector $$4\vec{Q}$$. Since the resultant vector is just a scaled version of $$\vec{Q}$$, they are in the same direction. The angle between any vector and another vector that is a scaled version of the first vector is always $$0^\circ$$, because they are parallel to each other.

Therefore, the angle between $$\vec{Q}$$ and the resultant of $$(2 \vec{Q}+2 \vec{P})$$ and $$(2 \vec{Q}-2 \vec{P})$$ is $$0^\circ$$.

So, the correct option is:

Option B: $$0^\circ$$

Comments (0)

Advertisement