Question

If \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + \hat{j} - \hat{k} \), then \( \vec{a} \) and \( \vec{b} \) are:

• A. collinear vectors which are not parallel
• B. parallel vectors
• C. perpendicular vectors
• D. unit vectors

Hint:

Two vectors are perpendicular if their dot product equals zero.

Answer 1

The Correct Option is C

Step 1: Calculate the dot product of \( \vec{a} \) and \( \vec{b} \).
The dot product is computed as: \[ \vec{a} \cdot \vec{b} = (2)(1) + (-1)(1) + (1)(-1) = 2 - 1 - 1 = 0. \]
Step 2: Determine perpendicularity.
Vectors are perpendicular if their dot product equals 0. 
Step 3: State the conclusion.
Based on the calculation, vectors \( \vec{a} \) and \( \vec{b} \) are perpendicular.