Quiz

Lines and Planes in Space — Lesson quiz

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What are the possible positions of two lines in space?

Parallel, intersecting, or skew

Parallel or intersecting only

Intersecting or skew only

Perpendicular or parallel only

Can two skew lines lie in one plane?

Yes, because they do not intersect

Yes, if they are parallel

No, because two lines in one plane must either intersect or be parallel

No, because they can never be parallel

What is the condition for a line to be perpendicular to a plane?

It is perpendicular to just one line in the plane

It is parallel to any line in the plane

It meets the plane at exactly one point

It is perpendicular to two intersecting lines lying in the plane

In a cube of edge 4 cm with A(0, 0, 0), B(4, 0, 0), G(4, 4, 4) and H(0, 4, 4), are the lines AB and GH parallel?

No, because they are skew

Yes, because GH has direction (−4, 0, 0), a negative multiple of the direction (4, 0, 0) of AB, and both lie in plane ABGH

No, because they do not lie in one plane

Yes, because they are perpendicular

Find the length of the space diagonal AG of a cube of edge 5 cm.

5√2 ≈ 7.07 cm

5√3 ≈ 8.66 cm

10 cm

25 cm

In a cube of edge 4 cm, G lies directly above C. Find the distance from G to the plane ABCD.

4√2 cm

8 cm

0 cm

4 cm