Larson_Calculus_10e ch11sec02
MULTIPLE CHOICE
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.
or 6.4031 to four decimal places.
b.
or 6.3246 to four decimal places.
c.
or 6.4807 to four decimal places.
d.
or 5.9161 to four decimal places.
e.
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.
41
2 10
42
43
43
d.
e.
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.
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.
12. Given , sketch the graph of .
a.
b.
c.
d.
e.
13. Find the vector
, ,
a.
b.
c.
d.
e.
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/ )
b.
(1/ )
c.
1/ )
d.
(1/ )
e.
1/ )
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.
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.
77
59
59
77
6 2
a.
b.
c.
d.
e.