Practice: Lines & Planes

10 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

A line through

P (1, 0, 2)

parallel to

v = ⟨ 2, - 1, 3 ⟩

has parametric equations

Q2.

basic

Two lines have direction vectors

v_{1} = ⟨ 1, 2, 3 ⟩

and

v_{2} = ⟨ - 2, - 4, - 6 ⟩

. They are

Q3.

basic

An equation of the plane through

(1, 2, 3)

with normal

n = ⟨ 4, 0, - 1 ⟩

Q4.

intermediateFinal Review #27

The distance from the point

(1, 2, 3)

to the plane

x + 4 y - z = 2

Q5.

basic

The line through

(1, 0, - 2)

in the direction

⟨ 0, 0, 1 ⟩

Q6.

basic

Two planes are parallel iff

Q7.

intermediateFinal Review #26

Find the line of intersection direction for planes

2 x + y - z = 0

and

- x + y + z = 1

Q8.

intermediate

If two lines have direction vectors

v_{1}

and

v_{2}

with

v_{1} \cdot v_{2} = 0

, the lines are

Q9.

intermediateFinal Review #28

Distance between the parallel planes

3 x + y - 4 z = 2

and

3 x + y - 4 z = 24

Q10.

basic

True/False: Two planes that are not parallel must intersect in a line.