Deck 11: Vectors and the Geometry of Space

Question 1

Suppose a gun with a muzzle velocity of 1200 feet per second is fired at an angle of above the horizontal.Find the horizontal component of the velocity.Round your answer to two decimal places.

A) ft/sec
B) ft/sec
C) ft/sec
D) ft/sec
E)ft/sec

Answer 1

ft/sec

Question 2

Find the magnitude of the vector given below.Round your answer to four decimal places.

A)
B)
C)
D)
E)

Answer 2

Question 3

Suppose a plane flies at a constant groundspeed of 600 miles per hour due east and encounters a 10 mile-per-hour wind from the northwest.Both the airspeed and the compass direction
Must change to for the plane to maintain its groundspeed and eastward direction.Find the airspeed to
Maintain its groundspeed and eastward direction.Round your answer to two decimal places.

A)
B)
C)
D)
E)

Answer 3

Question 4

Suppose a plane is flying in the direction (relative to the west).Its speed with respect to the air is 600 kilometers per hour.The wind at the plane's altitude is from the southwest at
80 kilometers per hour (see figure).What is its speed with respect to the ground? Round your answer
To one decimal place.

A)
B)
C)
D)
E)

Question 5

To carry a 500-pound cylindrical weight, two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder.One rope makes a angle away from the vertical
And the other makes a angle as shown in the figure below.Find the vertical component of each
Worker's force.Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 6

The vector v and its initial point is given.Find the terminal point. , initial point

A)
B)
C)
D)
E)

Question 7

Given

A)
B)
C)
D)
E)

Question 8

Find the unit vector in the direction of u.

A)
B)
C)
D)
E)

Question 9

Find vectors u and v whose initial and terminal points are given.Determine whether u and v are equivalent.
U: (6,5), (9,11) v: (3,-5), (6,1)

A)
B)
C)
D)
E)

Question 10

Three forces with magnitudes pounds, pounds and pounds act on an object at angles respectively, with the positive x-axis.Find the direction and magnitude
Of the resultant force.(The choices below are given to two decimal places.)

A) with the positive x-axis
B) with the positive x-axis
C) with the positive x-axis
D) with the positive x-axis
E)with the positive x-axis

Question 11

Find the component form of vector u + v given and the angles that u and v make with the positive x-axis are

A)
B)
C)
D)
E)

Question 12

To carry a 100-pound cylindrical weight, two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder.One rope makes a angle away from the vertical
And the other makes a angle as shown in the figure below.Find each rope's tension if the resultant
Force is vertical.Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 13

Given

A)
B)
C)
D)
E)

Question 14

Find the vector v with the given magnitude and the same direction as

A)
B)
C)
D)
E)

Question 15

Find the vector v whose initial and terminal points are given below. (5,5), (7,2)

A)
B)
C)
D)
E)

Question 16

Given

A)
B)
C)
D)
E)

Question 17

Suppose a plane is flying in the direction Its speed with respect to the air is 900 kilometers per hour.The wind at the plane's altitude is from the southwest at 100 kilometers per hour
(see figure).What is the true direction of the plane? Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 18

Suppose a plane flies at a constant groundspeed of 500 miles per hour due east and encounters a 50 mile-per-hour wind from the northwest.Both the airspeed and the compass direction
Must change to for the plane to maintain its groundspeed and eastward direction.Find the airspeed to
Maintain its groundspeed and eastward direction.Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 19

Find the vector v whose initial and terminal points are given below. (5.5,2.1), (9.5, 6.1)

A)
B)
C)
D)
E)

Question 20

Find the component form of vector v given its magnitude is and the angle it makes with the positive x-axis is

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)

Question 22

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

A)
B)
C)
D)
E)

Question 23

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 24

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)

Question 25

Find a unit vector u in the direction opposite of

A)
B)
C)
D)
E)

Question 26

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

A)
B)
C)
D)
E)

Question 27

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 28

Given

A)
B)
C)
D)
E)

Question 29

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

A)
B)
C)
D)
E)

Question 30

Given sketch the graph of

A)
B)
C)
D)
E)

Question 31

Find the magnitude of the vector given below.

A)
B)
C)
D)
E)

Question 32

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 33

Find the vector

A)
B)
C)
D)
E)

Question 34

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)
D) or 4.0000
E) r 8.0000

Question 35

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

A)
B)
C)
D)
E)

Question 36

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)

Question 37

Find the vector v with the magnitude and direction of

A)
B)
C)
D)
E)

Question 38

Find the unit vector in the direction of

A)
B)
C)
D)
E)

Question 39

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)