11.2 Space Coordinates and Vectors in Space 655
11.2 Space Coordinates and Vectors in Space
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the coordinates of the point that is located 4 units behind the yz-plane, 6 units to
the left of xz-plane, and 4 units above the xy-plane.
a. (–4,–6,–4)
b. (–4,6,4)
c. (4,–6,4)
d. (–4,6,–4)
e. (–4,–6,4)
____ 2. Find the distance between the points given below.
(–4, 2, –3 ), ( 0, 5, 1 )
a.
41
or 6.4031 to four decimal places.
b.
210
or 6.3246 to four decimal places.
c.
42
or 6.4807 to four decimal places.
d.
43
or 5.9161 to four decimal places.
e.
43
or 6.5574 to four decimal places.
____ 3. Find the coordinates of the midpoint of the line segment joining the points given
below.
(4, 8, 4), (7, 10, 7)
a. (5.5, 1, 5.5)
b. (1.5, 1, 5.5)
c. (1.5, 9, 5.5)
d. (1.5, 9, 1.5)
e. (5.5, 9, 5.5)
____ 4. Find the standard equation of the sphere with center (2, 8, 4), and radius 2.
a.
b.
c.
d.
e.
656 Chapter 11: Vectors and the Geometry of Space
____ 5. Find the standard equation of a sphere that has diameter with the end points given
below.
(3, –2, 4), (7, 12, 4)
a.
b.
c.
d.
e.
____ 6. Find the standard equation of the sphere with center at and tangent to the
yz-plane.
a.
b.
c.
d.
e.
____ 7. Complete the square to write the following equation in the standard form for a
sphere.
a.
b.
c.
d.
e.
11.2 Space Coordinates and Vectors in Space 657
____ 8. Find the component form of the vector u with the given initial and terminal points.
Initial point: (5, 7, 8 )
Terminal point: (–2 , 10 , 10 )
a.
b.
c.
d.
e.
____ 9. Find the magnitude of the vector v given its initial and terminal points. Round your
answer to four decimal places.
Initial point: (–2, –4, –5)
Terminal point: (–3, –9, –10)
a. or 7.3485
b. or 7.4833
c. or
d. or 4.0000
e. or 8.0000
____ 10. Given the vector v and its initial point find the terminal point of the vector.
, initial point
a.
b.
c.
d.
e.
____ 11. Given , find .
a.
b.
c.
d.
e.
658 Chapter 11: Vectors and the Geometry of Space
____ 12. Given , sketch the graph of .
a.
b.
c.
11.2 Space Coordinates and Vectors in Space 659
d.
e.
____ 13. Find the vector
, ,
a.
b.
c.
d.
e.
660 Chapter 11: Vectors and the Geometry of Space
____ 14. Find the magnitude of the vector given below.
a.
b.
c.
d.
e.
____ 15. Find the unit vector in the direction of u.
a.
b.
c.
d.
e.
____ 16. Find a unit vector u in the direction opposite of .
a. 1/
77
)
b. (1/
59
)
c. 1/
59
)
d. (1/
77
)
e. 1/
62
)
11.2 Space Coordinates and Vectors in Space 661
____ 17. Find the vector v with the magnitude and direction of .
a.
b.
c.
d.
e.
____ 18. Given the vector v lies in the yz-plane, has magnitude 8, and makes an angle of
with the positive y-axis. Find the component form of v.
a.
b.
c.
d.
e.
662 Chapter 11: Vectors and the Geometry of Space
____ 19. Suppose the guy wire to a 100-foot tower has a tension of 500 pounds. Using the
distances shown in the figure, write the component form of the vector F representing the tension in
the wire. Round numerical values in your answer to the nearest integer.
a.
b.
c.
d.
e.
11.2 Space Coordinates and Vectors in Space 663
11.2 Space Coordinates and Vectors in Space
Answer Section