Question

If $\theta$ is an angle given by $\cos \theta$ $=$ $\frac{{\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma }{{\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma }$ where $\alpha$, $\beta$, $\gamma$ are the angles made by a line with the positive directions of the axes of reference then the measure of $\theta$ is

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is D $\frac{\pi }{3}$

The cosines of the angles made by a directed line segment with the coordinate axes are called as the direction cosines of that line.

if $\alpha ,\beta ,\gamma$ are the angles made by the line segment with the coordinate axis then these angles are termed to be the direction angles and the cosines of these angles are the direction cosines of the line.

cos α, cos β and cos γ are called as the direction cosines

hence from the above diagram it is known that $\theta$ is equal to $60c^0=\frac{\pi }{3}$.