Chapter 11.4, Problem 72E

a.

To determine

To find: The angle between normal vectors of given two planes.

Answer to Problem 72E

  $\theta ={65}^0$

Explanation of Solution

Given information:

Two planes and their normal vectors are shown below.

  

Calculation:

Two planes and their normal vectors are shown below.

  

Since, angle between normal vectors of two plane is same as angle between two plane.

From above sketch angle between two normal vector will be equal to $\theta ={65}^0$

b.

To determine

To find: The angle between a third plane parallel to ${\text{n}}_1$ and the blue plane.

Answer to Problem 72E

  $\theta ={90}^0$

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Calculation:

Two planes and their normal vectors are shown below.

  

  ${\text{n}}_1$ is the normal vector to the blue plane.

So, a third plane parallel to the ${\text{n}}_1$ will also be normal to the blue plane.

From above sketch the angle between a third plane parallel to ${\text{n}}_1$ and the blue plane will be equal to $\theta ={90}^0$

c.

To determine

To find: The angle between a third plane parallel to ${\text{n}}_2$ and the blue plane.

Answer to Problem 72E

  ${25}^0$

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Calculation:

Two planes and their normal vectors are shown below.

  

Angle between ${\text{n}}_2$ and the blue plane is $\left(90-\theta \right)={25}^0$ .

So, a third plane parallel to the ${\text{n}}_2$ will have same angle with blue plane as ${\text{n}}_2$ .

From above sketch the angle between a third plane parallel to ${\text{n}}_2$ and the blue plane will be equal to $\left(90-\theta \right)={25}^0$