Question

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. \(30^{\circ }\)
• C. \(60^{\circ }\)
• D. \(0^{\circ }\)

Hint:

Find the vector P - Q first and compare its direction with P.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The angle between two vectors depends only on their directions. Parallel vectors in the same direction make an angle of \(0^{\circ}\).

Step 2: Calculation
\(\vec{P}-\vec{Q}=(\hat{i}+\hat{j}+\hat{k})-(-\hat{i}-\hat{j}-\hat{k})=2(\hat{i}+\hat{j}+\hat{k})\)

Step 3: Compare with P
\(\vec{P}-\vec{Q}=2\vec{P}\), so it is a positive multiple of \(\vec{P}\). Hence the angle between them is \(0^{\circ}\).

Final Answer:
The angle between the two vectors is zero degrees. \[ \boxed{\text{(D) }0^{\circ}} \]