Chapter 6, Problem 9RP

Solution

a

To check, whether the plane “ r ” is perpendicular to the plane “ m ”.

True

Given information:

  $\overleftrightarrow{AB}$ is parallel to plane m and perpendicular to plane r, $\overleftrightarrow{CD}$ lies in r is provided in the question which will help to find the solution.

Explanation:

It is given that the plane “ r ” and plane “ m ” are perpendicular to each other. Therefore, this is

correct option.

Hence, $r\perp m$

b

To check, whether the plane “ r ” is parallel to the plane “ m ”.

False

Given information:

  $\overleftrightarrow{AB}$ is parallel to plane m and perpendicular to plane r, $\overleftrightarrow{CD}$ lies in r is provided in the question which will help to find the solution.

Explanation:

It is given that the plane “ r ” and plane “ m ” are perpendicular to each other. Therefore, they

cannot be parallel to each other.

c

To check, whether the plane line segment CD is perpendicular to the plane “ m ”.

True

Given information:

  $\overleftrightarrow{AB}$ is parallel to plane m and perpendicular to plane r, $\overleftrightarrow{CD}$ lies in r is provided in the question which will help to find the solution.

Explanation:

Since the line segment $\overleftrightarrow{CD}$ lies in the plane “ r ” which is perpendicular to the plane “ m ”.

Therefore, $\overleftrightarrow{CD}$$\perp m$

d

To check, whether the plane line segment AB is parallel to the line CD.

False

Given information:

  $\overleftrightarrow{AB}$ is parallel to plane m and perpendicular to plane r, $\overleftrightarrow{CD}$ lies in r is provided in the question which will help to find the solution.

Explanation:

Since the line segment $\overleftrightarrow{CD}$ lies in the plane “ r ” which is perpendicular to the plane “ m ”, and $\overleftrightarrow{AB}$ lies in the plane “ m ”. Therefore, $\overleftrightarrow{AB}$ can’t be parallel to $\overleftrightarrow{CD}$ .

e

To check, the lines segment $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are skew or not.

True

Given information:

  $\overleftrightarrow{AB}$ is parallel to plane m and perpendicular to plane r, $\overleftrightarrow{CD}$ lies in r is provided in the question which will help to find the solution.

Explanation:

Since the line segment $\overleftrightarrow{CD}$ lies in the plane “ r ” which is perpendicular to the plane “ m ”, and $\overleftrightarrow{AB}$ lies in the plane “ m ”.

Since, the lines are in different planes, therefore, it will neither intersect nor parallel. Hence the lines will be skew.