Q111 / 150 · MHT CET 2026 (16 April Shift 1) · Physics
Let $\vec{P} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{Q} = -(\hat{i} + \hat{j} + \hat{k})$. The angle between $(\vec{P} - \vec{Q})$ and $\vec{P}$ is
- A$90^\circ$
- B$60^\circ$
- Correct answerC$0^\circ$
- D$30^\circ$
Solution
Given $\vec{P} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{Q} = -(\hat{i} + \hat{j} + \hat{k})$.
We can write $\vec{Q} = -\vec{P}$.
Calculating the vector $(\vec{P} - \vec{Q})$:
$\vec{P} - \vec{Q} = \vec{P} - (-\vec{P}) = 2\vec{P}$
Since $(\vec{P} - \vec{Q})$ is a positive scalar multiple of $\vec{P}$, the two vectors are parallel and point in the same direction.
Therefore, the angle between $(\vec{P} - \vec{Q})$ and $\vec{P}$ is $0^\circ$.
Answer: $0^\circ$
We can write $\vec{Q} = -\vec{P}$.
Calculating the vector $(\vec{P} - \vec{Q})$:
$\vec{P} - \vec{Q} = \vec{P} - (-\vec{P}) = 2\vec{P}$
Since $(\vec{P} - \vec{Q})$ is a positive scalar multiple of $\vec{P}$, the two vectors are parallel and point in the same direction.
Therefore, the angle between $(\vec{P} - \vec{Q})$ and $\vec{P}$ is $0^\circ$.
Answer: $0^\circ$
Hence, the correct answer is option: 'C'.