Question

If angle between line and plane is $\theta$ then the angle between line and the normal to plane is $\frac{\pi }{2}-\theta$

• A. True
• B. False

Answer 1

The correct option is A True


We know that the normal to a plane makes ${90}^{\circ }$ angle from the plane. So referring to the diagram above $\alpha +\beta ={90}^{\circ }$. Where $\alpha$ is the angle made by the line from the plane and $\beta$ is the angle made by the line from the normal of the plane. $\beta ={90}^{\circ }-\alpha$.
Therefore we can say, if a line makes $\theta$ angle with the plane then the angle made by line with it’s normal will be nothing but ${90}^{\circ }-\theta$ or $\frac{\pi }{2}-\theta$.