The angles which a vector \(\hat{i} + \hat{j} + \sqrt{2} \h…

Physics Vectors Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: September 12, 2026

The angles which a vector \(\hat{i} + \hat{j} + \sqrt{2} \hat{k}\) makes with X, Y and Z axes respectively are

60°, 60°, 60°

45°, 45°, 45°

60°, 60°, 45°

45°, 45°, 60°

Text Solution

Verified by Experts

The correct answer is:

\(\vec{R} = \hat{i} + \hat{j} + \sqrt{2} \hat{k}\)

Comparing the given vector with \(\mathbf{R} = R_x \hat{i} + R_y \hat{j} + R_z \hat{k}\)

\(R_x = 1, R_y = 1, R_z = \sqrt{2}\) and \(\left|\vec{R}\right| = \sqrt{R_x^2 + R_y^2 + R_z^2}\) = 2

\(\cos \alpha = \frac{R_x}{R} = \frac{1}{2} \Rightarrow \alpha = 60^\circ\)

\(\cos \beta = \frac{R_y}{R} = \frac{1}{2} \Rightarrow \beta = 60^\circ\)

\(\cos \gamma = \frac{R_z}{R} = \frac{1}{\sqrt{2}} \Rightarrow \gamma = 45^\circ\)

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