QJEEM24Ph8f38: JEE Main 2024 Physics - Class 11 JEEM24Ph8f38 Solution: The angle between vector and the resultant of and is :

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:

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: $0^\circ$