Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

The angle between $\vec{a}$ and the plane of $\vec{b},\vec{c}$ is the angle between $\vec{a}$ and $\vec{b}+\vec{c}(\vec{b}+\vec{c}$ lies along the angular bisector of $\vec{b}$ and $\vec{c}$, in that plane). $\cos \theta =\frac{\vec{a}\cdot (\vec{b}+\vec{c})}{|\vec{a}||\vec{b}+\vec{c}|}=\frac{2\cos \alpha }{\sqrt{2+2\cos \alpha }}=\frac{\cos \alpha }{\cos \frac{\alpha }{2}}$.