Question 37: Motion in 2D & Vectors

Question

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

Accepted Answer

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:
$$
	ext{Resultant} = (2 \vec{Q}+2 \vec{P}) + (2 \vec{Q}-2 \vec{P}) = 4 \vec{Q}
$$
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: $$0^\circ$$

Answer

$$
	an ^{-1}(\mathrm{P} / \mathrm{Q})
$$

Answer

0$$^\circ$$

Answer

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

Answer

$$
	an ^{-1}(2 Q / \mathrm{P})
$$

Motion in 2D & Vectors

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

Choose the correct answer: