Chapter 3.6, Problem 40PPS

(a)

To determine

To Find: What must be true if both lines $aandb$ are perpendicular to the plane $P$ .

Answer to Problem 40PPS

  $a,b\in Q$

Explanation of Solution

Given:

  

Since the line $aandb$ are perpendicular to the plane $P$ that means the points $aandb$ are coplanar.

The points $aandb$ lie on the plane $Q.$

Thus

  $a,b\in Q$

(b)

To determine

To Find: What must be true if planes $RandQ$ are parallel and intersect to the plane $P$ .

Answer to Problem 40PPS

  $c\parallel d$

Explanation of Solution

Given:

  

Since planes $RandQ$ are parallel and intersect to the plane $P$ .

Thus lines $candd$ are parallel.

I.e.

  $c\parallel d$

(c)

To determine

To Find: What must be true if planes $RandQ$ are perpendicular to line $l$ .

Answer to Problem 40PPS

  $R\parallel Q$

Explanation of Solution

Given:

  

Since planes $RandQ$ are perpendicular to line $l$ that means the planes are parallel.

Thus

  $R\parallel Q$