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Physics · MOTION IN A PLANE
हिन्दीA vector \( \mathbf{A} \) in three dimensions makes angles \( \alpha = 60^\circ \) and \( \beta = 60^\circ \) with the x and y axes respectively. What angle \( \gamma \) does it make with the z-axis?
Correct answer · Option 4
\( 45^\circ \)
Explanation
\( \cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1 \Rightarrow \cos^2 60^\circ + \cos^2 60^\circ + \cos^2\gamma = 1 \Rightarrow \frac{1}{4} + \frac{1}{4} + \cos^2\gamma = 1 \Rightarrow \cos^2\gamma = \frac{1}{2} \Rightarrow \gamma = 45^\circ \).
