Question

1. use the diagram to the right to name the following. a) the intersection of lines l and m. b) another name for plane q. c) are points d and e collinear or coplanar? d) how many times do planes p and q intersect?

Explanation:

Step1: Identify intersection of lines

Lines \(l\) and \(m\) intersect at point \(E\).

Step2: Rename plane

Plane \(Q\) can also be named as plane \(EFG\) (since three non - collinear points determine a plane).

Step3: Check collinearity and coplanarity

Points \(D\) and \(E\) are not on the same line (so not collinear), and they lie on different planes (\(D\) in plane \(P\) and \(E\) in plane \(Q\)), so not coplanar.

Step4: Determine plane intersection

Two distinct planes \(P\) and \(Q\) intersect in a line. They intersect once.

Answer:

a) \(E\)
b) Plane \(EFG\)
c) Neither collinear nor coplanar
d) Once