Chapter 10.4, Problem 3E

To determine

To check: The planes are parallel, perpendicular or neither if $n_1\cdot n_2=0$ .

Answer to Problem 3E

The planes will be perpendicular if $n_1\cdot n_2=0$ .

Explanation of Solution

Given information:

Given that $n_1\cdot n_2=0$ .

Calculation:

The angle between two planes is given by,

  $\cos \theta =\frac{\left|n_1\cdot n_2\right|}{\Vert n_1\Vert \Vert n_2\Vert }$

Two planes with normal vector $n_1$ and $n_2$ are perpendicular when $n_1\cdot n_2=0$ .

Therefore, the planes will be perpendicular if $n_1\cdot n_2=0$ .