Number 
Question 
Answer 
See the work 
1.

What are the projections of the point (5, 6, 1) on the coordinate planes?
The xyplane:
The yzplane:
The xzplane: 
On the xyplane: (5, 6, 0)
On the yzplane: (0, 6, 1)
On the xzplane: (5, 0,1) 
The work
Point Cost: 0 
2.

Determine whether the three points P= (9, 3, 9), Q = (11, 7, 3),
R=(13, 13, 3) are colinear by computing the distances between pairs of points.

Distance from P to Q:
Distance from Q to R:
Distance from P to R:
Are the three points colinear (y/n)? N

The work
Point Cost: 2 
3.

What is the distance from the point (1, 5, 8)
to the xzplane?
Distance

5

The work
Point Cost: 0

4.

What do the following equations represent in R3?
Match the two sets of letters:
a. a vertical plane
b. a horizontal plane
c. a plane which is neither vertical nor horizontal
A. 7x+2y= 3
B. x = 3
C. y = 10
D. z = 8

A. a
B. a
C. a
D. b

The work 
5.

Find the equation of the sphere centered at (0,9,10) with radius 7. ______________= 0.
Give an equation which describes the intersection of this sphere with the plane z = 11. ______________= 0.


The work
Point Cost: 1 
6. 
Find the equation of the sphere if one of its
diameters has endpoints (10, 2, 9) and (11, 0, 6).
______________= 0.


The work
Point Cost: 2 
7.

Find an equation of the sphere that passes through the origin and whose center is (5, 6, 6). ________________= 0 

The work
Point Cost: 2 
8. 
Find an equation of the largest sphere with center (4, 8 , 6) that is contained completely in the first octant.
__________=0


The work
Point Cost: 3 
9.

Find the center and radius of the sphere
Center: ( _, _, _) Radius:_________

Center: ( 6, 9, 8)
Radius: 6

The work
Point Cost: 3 
10.

Write down an (in)equality which describes the solid ball of radius 5 centered at (6, 3, 3).
It should have a form like .

≤ 0

The work
Point Cost: 1 
11.

Find the distance from (3,6,11) to each of the following:
1. The xyplane:
2. The yzplane:
3. The xzplane:
4. The xaxis:
5. The yaxis:
6. The zaxis:


The work
Point Cost: 3 