Deck 11: Vectors in the Plane

Question 1

vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent.

Answer 1

C

Question 2

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

Answer 2

C

Question 3

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.

Answer 3

A

Question 4

the component form of vector v given its magnitude is

Question 5

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

Question 6

the vector v whose initial and terminal points are given below.

Question 7

Question 8

Question 9

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.

Question 10

the vector v whose initial and terminal points are given below.

Question 11

the component form of vector

Question 12

Question 13

Question 14

the distance between the points given below.

Question 15

Question 16

Suppose a gun with a muzzle velocity of 1200 feet per second is fired at an angle of

Question 17

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.

Question 18

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 19

carry a 100-pound cylindrical weight, two workers lift on the ends of short ropes

Question 20

carry a 500-pound cylindrical weight, two workers lift on the ends of short ropes

Question 21

the standard equation of the sphere with center at yz-plane.

Question 22

a unit vector u in the direction opposite of

Question 23

the unit vector in the direction of u.

Question 24

Question 25

the magnitude of the vector given below.

Question 26

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

Question 27

Question 28

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

Question 29

the coordinates of the midpoint of the line segment joining the points given below.

Question 30

the standard equation of a sphere that has diameter with the end points given below.

Question 31

Question 32

the angle between the vectors for u and v given below.

Question 33

A)-8
B)-4
C)4
D)7
E)-1

Question 34

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

Question 35

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)

Question 36

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.

Question 37

Question 38

the component form of the vector u with the given initial and terminal points. Initial point: (5, 7, 8 )
Terminal point: (-2 , 10 , 10 )

Question 39

Given the vector v lies in the yz-plane, has magnitude 8, and makes with the positive y-axis. Find the component form of v.

Question 40

the vector v with the magnitude

Question 41

Question 42

Determine whether u and v are orthogonal, parallel or neither.

Question 43

Question 44

Assume the only force to overcome is that due to gravity. Find the force perpendicular to the hill. Round your answer to one decimal place.

Question 45

Suppose a car is towed using a force of 1300 newtons. The chain used to pull the car makes a your answer to two decimal places.

A)9,426.60 km-N
B)4,712.80 km-N
C)4,726.80 km-N
D)9,424.60 km-N
E)2,197.61 km-N

Question 46

the direction cosines of the vector u given below.

Question 47

Question 48

object is pulled 5 feet horizontally across a floor, using a force of 95 pounds. The direction of the force is
Decimal places.

A)467.78 ft-lb
B)398.56 ft-lb
C)82.48 ft-lb
D)6.96 ft-lb
E)511.94 ft-lb

Question 49

the direction cosines of the vector u given below.

Question 50

Assume the only force to overcome is that due to gravity. Find the force required to keep the truck from rolling down the hill. Round your answer to two decimal places.

Question 51

Question 52

Question 53

Question 54

Question 55

the angle between the vectors for u and v.

Question 56

Suppose a toy wagon is pulled by exerting a force of 25 pounds on a handle that makes a angle with the horizontal as shown in the figure below. Find the work done in pulling
The wagon 50 feet. Round your answer to one decimal place.

Question 57

Determine whether u and v are orthogonal, parallel and pointing in the same direction, parallel and pointing in opposite directions, or neither.

Question 58

Question 59

the direction angles of the vector u given below. Round your answer to one decimal place.

Question 60

Question 61

a set of symmetric equations of the line through the points

Question 62

the area of a parallelogram that has the given vectors as adjacent sides. Round your answer to two decimal places.

Question 63

a set of parametric equations of the line that passes through the point

Question 64

Determine whether any of the lines given below are parallel or identical.

Question 65

the set of parametric equations of the line through the point

Question 66

a set of parametric equations of the line through the point

Question 67

the area of the triangle with the vertices

Question 68

Question 69

the volume of the parallelepiped with the following vertices.

Question 70

the magnitude and the direction of the force on a crankshaft change as the crankshaft rotates. Find the torque on the crankshaft using the position and data shown in the figure.
Round your answer to two decimal places.

Question 71

child applies the brakes on a bicycle by applying a downward force of 25 pounds

A)12.50 ft-lb
B)6.25 ft-lb
C)75.00 ft-lb
D)10.83 ft-lb
E)21.65 ft-lb

Question 72

a set of symmetric equations of the line through the point

Question 73

the triple scalar product to find the volume of the parallelepiped having adjacent edges given by the vectors

Question 74

Question 75

Determine whether the lines given below intersect, and, if so, find the point of intersection.

Question 76

the area of the parallelogram that has the given vectors adjacent sides.

Question 77

the area of the parallelogram with the vertices

Question 78

Question 79

a set of parametric equations of the line through the points

Question 80

Determine whether any of the lines given below are parallel or identical.