Chapter 6.2, Problem 16PSC

a

To determine

To prove: The segment ED and plane m are perpendicular

Answer to Problem 16PSC

Line segment $\overline{\text{DE}}$ will be perpendicular to given plane m

Explanation of Solution

Given information:

The points A, B, C & D given lie in given plane m

One given line is perpendicular to other given line, i.e., $\overleftrightarrow{\text{ED}}\perp \overleftrightarrow{\text{BC}}$

Since given,

Points A, B, C & D given lie in given plane m and

  $\overleftrightarrow{\text{ED}}\perp \overleftrightarrow{\text{BC}}$

Shows that a line, $\overleftrightarrow{\text{DE}}$ is perpendicular to plane than line, $\overline{\text{BC}}$ passing through its foot is perpendicular to it

Thus, only line segment $\overline{\text{DE}}$ will be perpendicular to given plane m

Hence proved

b

To determine

To find: The number of planes in the given figure

Answer to Problem 16PSC

There are two planes in the given figure

Explanation of Solution

Given information

The points A, B, C & D given lie in given plane m.

One given line is perpendicular to other given line, i.e., $\overleftrightarrow{\text{ED}}\perp \overleftrightarrow{\text{BC}}$

Since,

One plane, m is already given in the figure

Second plane will be where line segment lies and which is parallel to given plane, m.

Hence, there are two planes in the figure given