Question

Find the angle between the planes $3x-2y+6z-5=0$ and $2x-y-2z-7=0$.

Answer 1

$\begin{array}{c}3x-2y+6z-5=0\\ 2x-y-2z-7=0\\ \cos \theta =\frac{\left|6+2-12\right|}{\sqrt{49}\sqrt{9}}\\ \cos =\frac{4}{7\times 3}=\frac{4}{21}\\ \therefore ={\cos }^{-1}\left(\frac{4}{21}\right)\end{array}$