Show that the planes `2x+6y-6z=7\ a n d\ 3x+4y+5z=8` are at right angles.

Explanation

It is known that the planes `a_{1} x+b_{1} y+c_{1} z+d_{1}=0` and `a_{2} x+b_{2} y+c_{2} z+d_{2}=0` are at right angles,
if ` a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0`

Now, `(2)(3)+(6)(4)+(6)(-5)=0`

Therefore, planes `2 x+6 y+6 z=7 and 3 x+4 y-5 z=8` are at right angles.