JEE MAIN - Physics (2024 - 5th April Morning Shift - No. 18)
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: $$0^\circ$$
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