Question

Let \(\overset{⃗}{P} = \hat{i}+\hat{j}+\hat{k}\) and \(\overset{⃗}{Q} = -(\hat{i}+\hat{j}+\hat{k})\). The angle between \((\overset{⃗}{P}-\overset{⃗}{Q})\) and \(\overset{⃗}{P}\) is

• A. \(90^{\circ}\)
• B. \(60^{\circ}\)
• C. \(0^{\circ}\)
• D. \(30^{\circ}\)

Hint:

Since Q = -P, the vector P - Q equals 2P, which points along P.

Answer 1

The Correct Option is C

Step 1: A positive multiple:
Any vector of the form $k\vec P$ with $k>0$ points the same way as $\vec P$.

Step 2: Apply:
$\vec P - \vec Q = 2\vec P$ with $k = 2 > 0$.

Step 3: Result:
The two vectors are parallel with no angle between them, so the angle is $0^\circ$, option (C).

Final Answer:
The angle is 0 degrees. \[ \boxed{\text{(C) }0^{\circ}} \]