Chapter 10.4, Problem 64E

a.

To determine

To state: the angle between the normal vectors.

Answer to Problem 64E

The angle between the normal vectors is ${65}^{\circ }$ .

Explanation of Solution

Given information:

The figure provided in the question,

  

since, the angle between the both planes is ${65}^{\circ }$ , and the normal vectors are perpendiculars to the respective planes, so the angle between both normal vectors is ${65}^{\circ }$ .

b.

To determine

To state: the angle between the blue plane and the third plane which is parallel to $n_1$ .

Answer to Problem 64E

The angle between the blue plane and the third plane which is parallel to $n_1$is ${90}^{\circ }$ .

Explanation of Solution

Given information:

The figure provided in the question,

  

since, the angle between the $n_1$ and the blue plane is ${90}^{\circ }$ and the third plane is parallel to the normal vector $n_1$ .

Thus, the angle between the blue plane and the third plane which is parallel to $n_1$is ${90}^{\circ }$ .

c.

To determine

To state: the angle between the blue plane and the fourth plane which is parallel to $n_2$ .

Answer to Problem 64E

The angle between the blue plane and the fourth plane which is parallel to $n_2$is ${25}^{\circ }$ .

Explanation of Solution

Given information:

The figure provided in the question,

  

since, the angle between the $n_2$ and blue plane is ${25}^{\circ }$ and the fourth plane is parallel to the $n_2$ .

Thus, the angle between the blue plane and the fourth plane which is parallel to $n_2$is ${25}^{\circ }$ .