Deck 11: Section 2: Vectors and the Geometry of Space

Question 1

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)

Answer 1

(5.5, 9, 5.5)

Question 2

Find the standard equation of the sphere with center at and tangent to the yz-plane.

A)
B)
C)
D)
E)

Answer 2

Question 3

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)

Answer 3

Question 4

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.

Question 5

Given , find .

A)
B)
C)
D)
E)

Question 6

Find a unit vector u in the direction opposite of .

A) 1/ )
B) (1/ )
C) 1/ )
D) (1/ )
E) 1/ )

Question 7

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)

Question 8

Given the vector v and its initial point find the terminal point of the vector. , initial point

A)
B)
C)
D)
E)

Question 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

Question 10

Find the unit vector in the direction of u.

A)
B)
C)
D)
E)

Question 11

Find the vector v with the magnitude and direction of .

A)
B)
C)
D)
E)

Question 12

Find a point such that the points and are collinear.

A)
B)
C)
D)
E)

Question 13

Given , sketch the graph of .

A)
B)
C)
D)
E)

Question 14

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)

Question 15

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)

Question 16

Determine all the values of c that satisfy the equation given

A)
B)
C)
D)
E)

Question 17

Complete the square to write the following equation in the standard form for a sphere.

A)
B)
C)
D)
E)

Question 18

Find the magnitude of the vector given below.

A)
B)
C)
D)
E)

Question 19

Find the standard equation of the sphere with center (2, 8, 4), and radius 2.

A)
B)
C)
D)
E)

Question 20

Find the vector , ,

A)
B)
C)
D)
E)

Question 21

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)