Practice: 3D Space

10 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

What is the distance between

(2, 0, - 1)

and

(0, 3, 2)

Q2.

basicFinal Review style

Which equation describes a sphere with center

(1, - 2, 3)

and radius

4

Q3.

basic

Identify the surface in

R^{3}

y^{2} + z^{2} = 9

Q4.

basic

What region in

R^{3}

is described by

0 \leq z \leq 2

and

x^{2} + y^{2} \leq 1

Q5.

basic

The midpoint of segment from

(4, - 1, 0)

(- 2, 5, 6)

Q6.

intermediate

Complete the square:

x^{2} + y^{2} + z^{2} - 4 x + 6 y - 2 z = 11

describes a sphere with center and radius:

Q7.

basic

P = (3, 4, 12)

, what is

∣ O P ∣

(distance from

P

to the origin)?

Q8.

basic

Which equation describes the plane parallel to the

x y

-plane and 5 units below it?

Q9.

intermediate

True or False: The equation

x^{2} + y^{2} + z^{2} + 2 x - 4 y + 6 z + 20 = 0

describes a real sphere.

Q10.

intermediateFinal Review T/F

True/False: The set

{(x, y, z) ∣ x^{2} + y^{2} = 1}

R^{3}

is a **circle**.