Question

If \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} - 2\hat{j} + \hat{k} \), 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 is zero.

Answer 1

The Correct Option is C

To determine if \( \vec{a} \) and \( \vec{b} \) are perpendicular, calculate their dot product. The calculation is as follows: \[ \vec{a} \cdot \vec{b} = (2)(1) + (-1)(-2) + (1)(1) = 2 + 2 + 1 = 0. \] Because \( \vec{a} \cdot \vec{b} = 0 \), the vectors are perpendicular.
Final Answer: \( \boxed{{Perpendicular vectors}} \)