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:
Show Hint
- collinear vectors which are not parallel
- parallel vectors
- perpendicular vectors
- unit vectors
The Correct Option is C
Solution and Explanation
Step 1: Find the dot product of \( \vec{a} \) and \( \vec{b} \)
The dot product of \( \vec{a} \) and \( \vec{b} \) is: \[ \vec{a} \cdot \vec{b} = (2)(1) + (-1)(1) + (1)(-1) = 2 - 1 - 1 = 0. \]
Step 2: Check for perpendicularity
If \( \vec{a} \cdot \vec{b} = 0 \), the vectors are perpendicular.
Step 3: Conclude the result
The vectors \( \vec{a} \) and \( \vec{b} \) are perpendicular.
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