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Deck 11: Section 4: Vectors and the Geometry of Space
Full screen (f)
Question
Sketch the graph of the cross product of the unit vector 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Given 
and 
find 
.
A)
B)
C)
D)
E)
and find .A)
B)
C)
D)
E)
Question
Find the area of the parallelogram with the vertices 
, and 
. Round your answer to two decimal places.
A) 35.00
B) 3.00
C) 5.92
D) 7.00
E) 2.65
, and . Round your answer to two decimal places.A) 35.00
B) 3.00
C) 5.92
D) 7.00
E) 2.65
Question
Given 
, find 
.
A)
B)
C)
D)
E)
, find .A)
B)
C)
D)
E)
Question
Given 
and 
find 
.
A)
B)
C)
D)
E)
and find .A)
B)
C)
D)
E)
Question
Find the cross product of the unit vector 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Both 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. 
A) 2,598.08 ft-lb
B) 259.81 ft-lb
C) 212.13 ft-lb
D) 519.62 ft-lb
E) 150.00 ft-lb
A) 2,598.08 ft-lb
B) 259.81 ft-lb
C) 212.13 ft-lb
D) 519.62 ft-lb
E) 150.00 ft-lb
Question
Find a unit vector that is orthogonal to both 
and 
.
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
Question
Find the area of a parallelogram that has the given vectors as adjacent sides. Round your answer to two decimal places. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given by the vectors 
A)
B)
C)
D) 516
E)
A)
B)
C)
D) 516
E)
Question
A child applies the brakes on a bicycle by applying a downward force of 25 pounds on the pedal when the crank makes a 
angle with the horizontal (see figure). The crank is 6 inches in length. Find the torque at P. Round your answer to two decimal places. 
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
angle with the horizontal (see figure). The crank is 6 inches in length. Find the torque at P. Round your answer to two decimal places. 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
Find the area of the triangle with the vertices 
and 
. Round your answer to two decimal places.
A) 20.00
B) 8.00
C) 6.00
D) 2.24
E) 4.47
and . Round your answer to two decimal places.A) 20.00
B) 8.00
C) 6.00
D) 2.24
E) 4.47
Question
Find the volume of the parallelepiped with the following vertices. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the triple scalar product 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Following are the vertices of the parallelogram. Find the coordinates of the fourth vertex. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the area of the parallelogram that has the given vectors 
and 
as adjacent sides.
A)
B)
C)
D)
E)
and as adjacent sides.A)
B)
C)
D)
E)
Question
Given 
and 
, find 
.
A)
B)
C)
D)
E)
and , find .A)
B)
C)
D)
E)
Question
Given 
and 
, find 
.
A)
B)
C)
D)
E)
and , find .A)
B)
C)
D)
E)
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Deck 11: Section 4: Vectors and the Geometry of Space
1
Sketch the graph of the cross product of the unit vector .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
2
Given and find .
A)
B)
C)
D)
E)
and find .A)
B)
C)
D)
E)
3
Find the area of the parallelogram with the vertices , and . Round your answer to two decimal places.
A) 35.00
B) 3.00
C) 5.92
D) 7.00
E) 2.65
, and . Round your answer to two decimal places.A) 35.00
B) 3.00
C) 5.92
D) 7.00
E) 2.65
5.92
4
Given , find .
A)
B)
C)
D)
E)
, find .A)
B)
C)
D)
E)
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5
Given and find .
A)
B)
C)
D)
E)
and find .A)
B)
C)
D)
E)
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6
Find the cross product of the unit vector .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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7
Both 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.
A) 2,598.08 ft-lb
B) 259.81 ft-lb
C) 212.13 ft-lb
D) 519.62 ft-lb
E) 150.00 ft-lb
A) 2,598.08 ft-lb
B) 259.81 ft-lb
C) 212.13 ft-lb
D) 519.62 ft-lb
E) 150.00 ft-lb
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Unlock for access to all 18 flashcards in this deck.
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8
Find a unit vector that is orthogonal to both and .
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
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9
Find the area of a parallelogram that has the given vectors as adjacent sides. Round your answer to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 18 flashcards in this deck.
Unlock Deck
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10
Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given by the vectors
A)
B)
C)
D) 516
E)
A)
B)
C)
D) 516
E)
Unlock Deck
Unlock for access to all 18 flashcards in this deck.
Unlock Deck
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11
A child applies the brakes on a bicycle by applying a downward force of 25 pounds on the pedal when the crank makes a angle with the horizontal (see figure). The crank is 6 inches in length. Find the torque at P. Round your answer to two decimal places.
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
angle with the horizontal (see figure). The crank is 6 inches in length. Find the torque at P. Round your answer to two decimal places. 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
Unlock Deck
Unlock for access to all 18 flashcards in this deck.
Unlock Deck
k this deck
12
Find the area of the triangle with the vertices and . Round your answer to two decimal places.
A) 20.00
B) 8.00
C) 6.00
D) 2.24
E) 4.47
and . Round your answer to two decimal places.A) 20.00
B) 8.00
C) 6.00
D) 2.24
E) 4.47
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Unlock for access to all 18 flashcards in this deck.
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13
Find the volume of the parallelepiped with the following vertices.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Find the triple scalar product .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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15
Following are the vertices of the parallelogram. Find the coordinates of the fourth vertex.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Find the area of the parallelogram that has the given vectors and as adjacent sides.
A)
B)
C)
D)
E)
and as adjacent sides.A)
B)
C)
D)
E)
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17
Given and , find .
A)
B)
C)
D)
E)
and , find .A)
B)
C)
D)
E)
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18
Given and , find .
A)
B)
C)
D)
E)
and , find .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 18 flashcards in this deck.
Unlock Deck
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Unlock for access to all 18 flashcards in this deck.
