General Physics - Vectors

Frage 1 von 20

1

We say that the displacement of a particle is a vector quantity. Our best justification for this assertion is

Wähle eine der folgenden:

displacement can be specified by a magnitude and a direction
operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments
a displacement is obviously not a scalar
displacement can be specified by three numbers
displacement is associated with motion, where velocity is a vector

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Frage 2 von 20

1

Which of the following is an accurate statement?

Wähle eine der folgenden:

A vector cannot have zero magnitude if one of its components is not zero
The magnitude of a vector can be less than the magnitude of one of its components.
If the magnitude of vector A is less than the magnitude of vector B, then the x-component of A is less than the x-component of B.
The magnitude of a vector can be positive or negative.

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Frage 3 von 20

1

In the given figure, express vector \(\vec S\) in terms of \(\vec M\) and \(\vec N\).

Wähle eine der folgenden:

\[\vec S = -\vec M - \vec N\]
\[\vec S = \vec N - \vec M\]
\[\vec S = \vec M + \vec N\]
\[\vec S = \vec M - \vec N\]

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Frage 4 von 20

3

Check all statements that are true.

Wähle eine oder mehr der folgenden:

The magnitude of a vector can never be less than the magnitude of one of its components
If the magnitude of vector \(\vec A\) is less than the magnitude of vector \(\vec B\) , then the x component of
\(\vec A\) is less than the x component of \(\vec B\).
If all the components of a vector are equal to 1, then that vector is a unit vector.
If \(|\vec A + \vec B|=A+B\) and \(|\vec A - \vec B|=A+B\), then \(\vec A\) and \(\vec B\) are parallel with each other.
If two vectors point in opposite directions, their cross product must be zero.
If two vectors are perpendicular to each other, their dot product must be zero.

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Frage 5 von 20

1

Which of the following diagram illustrates the relationship \(\vec c = \vec b - \vec a\)?

Wähle eine der folgenden:

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Frage 6 von 20

1

The vector \(\vec V_3\) in the diagram is equal to

Wähle eine der folgenden:

\(\vec V_1 - \vec V_2\)
\(\vec V_1 + \vec V_2\)
\(\vec V_2 - \vec V_1\)
\(\vec V_1 \cos \theta \)
\(\vec V_1 / (\cos \theta)\)

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Frage 7 von 20

1

Four vectors (\(\vec A, \vec B, \vec C, \vec D\)) all have the same magnitude. The angle \(\theta\) between the adjacent vectors is \(45^{\circ}\) as shown. The correct vector equation is

Wähle eine der folgenden:

\(\vec A - \vec B - \vec C + \vec D = 0\)
\(\vec B + \vec D - \sqrt{2}\vec C=0\)
\(\vec A + \vec B = \vec B + \vec D\)
\(\vec A + \vec B + \vec C + \vec D = 0\)
\((\vec A + \vec C)/\sqrt{2} = -\vec B\)

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Frage 8 von 20

1

Vectors \(\vec A\) and \(\vec B\) lie in the \(xy\) plane. We can deduce that \(\vec A=\vec B\) if

Wähle eine der folgenden:

\({A^2}_x+{A^2}_y={B^2}_x+{B^2}_y\)
\(A_x+A_y=B_x+B_y\)
\(A_x=B_x\) and \(A_y=B_y\)
\(\frac{A_y}{A_x}=\frac{B_x}{B_y}\)
\(A_x=B_y\) and \(A_y=B_x\)

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Frage 9 von 20

1

If the eastward component of vector \(\vec A\) is equal to the westward component of vector \(\vec B\) and their northward components are equal. Which one of the following statements about these two vectors is correct?

Wähle eine der folgenden:

Vector \(\vec A\) is parallel to vector \(\vec B\)
Vectors \(\vec A\) and \(\vec B\) point in opposite directions.
Vector \(\vec A\) is perpendicular to vector \(\vec B\)
The magnitude of vector \(\vec A\) is equal to the magnitude of \(\vec B\).
None of the statements.

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Frage 10 von 20

1

Which of the following operations will not change a vector?

Wähle eine der folgenden:

Translate it parallel to itself.
Rotate it
Multiply it by a constant factor.
Add a constant vector to it.
Translate it perpendicular to itself.
None of the choices.

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Frage 11 von 20

1

If \(\vec A\) and \(\vec B\) are nonzero vectors for which \(\vec A \cdot \vec B=0\), it must follow that

Wähle eine der folgenden:

\(\vec A \times \vec B=0\)
\(\vec A\) is parallel to \(\vec B\).
\(|\vec A \times \vec B|=AB\)
\(|\vec A \times \vec B|=1\)
None of the statements.

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Frage 12 von 20

2

For the vectors shown in the figure, find the magnitude and direction of vector product \(\vec A \times \vec C\), assuming that the quantities shown are accurate to two significant figures.

Wähle eine der folgenden:

16, directed into the plane
16, directed out of the plane
45, directed into the plane
45, directed out of the plane

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Frage 13 von 20

2

What is the vector product of \(\vec A = 2.00 \hat i + 3.00 \hat j + 1.00 \hat k\) and \(\vec B = 1.00 \hat i - 3.00 \hat j - 2.00 \hat k\)?

Wähle eine der folgenden:

\(-3.00 \hat i + 5.00 \hat j - 9.00 \hat k\)
\(-5.00 \hat i + 2.00 \hat j - 6.00 \hat k\)
\(5\)
\(2.00 \hat i -9.00 \hat j - 2.00 \hat k\)
\(-9\)

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Frage 14 von 20

2

What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?

Wähle eine der folgenden:

6.93
-6.93
4.00
-4.00
8.00
6.81

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Frage 15 von 20

2

Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes \(\vec F_1 = 1.0 N, \vec F_2 = 8.0\) and \(\vec F_3 = 7.0 N\), where N is the standard unit of force, what is the component of the net force \(\vec F_{net}=\vec F_1+ \vec F_2+\vec F_3\) parallel to the floor?

Wähle eine der folgenden:

2.5N
5.1N
6.0N
7.8N

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Frage 16 von 20

3

Vectors A and B are shown in the figure. Vector \(\vec C\) is given by \(\vec C = \vec B -\vec A\). The magnitude of vector \(\vec A\) is 16.0 units, and the magnitude of vector \(\vec B\) is 7.00 units. What is the angle of vector \(\vec C\), measured counterclockwise from the +x-axis?

Wähle eine der folgenden:

16.9°
22.4°
73.1°
287°
292°
68

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Frage 17 von 20

2

You walk 53 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

Wähle eine der folgenden:

63° N of E
50° N of E
57° N of E
69° N of E

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Frage 18 von 20

3

Vectors \(\vec A\) and \(\vec B\) are shown in the figure. What is \(|-5.00\vec A + 4.00 \vec B|\)?

Wähle eine der folgenden:

31.8
\(-32.0 \hat i - 2.00 \hat k\)
1028
34
\(-2.00\hat i - 32.0 \hat j\)

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Frage 19 von 20

3

If \(\vec A = 1.00 \hat i + 4.00 \hat j - 1.00 \hat k, \vec B = 3.00\hat i - 1.00 \hat j - 4.00 \hat k\) , and \(\vec C=-1.00\hat i + 1.00 \hat j\), then \(|(\vec A \times \vec B) \cdot \vec C|\)=?

Wähle eine der folgenden:

18
\(12.00 \hat i - 6.00 \hat j - 12\hat k\)
\(-3.00\hat i -4.00 \hat j-4.00\hat k\)
\(6.00 \hat i - 12.00 \hat j - 12\hat k\)
\(12\sqrt{3}\)
-7
7

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Frage 20 von 20

3

In the figure, the magnitude of vector \(\vec A\) is 18.0 units, and the magnitude of vector \(\vec B\) is 12.0 units. What vector \(\vec C\) (magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive) must be added to the vectors \(\vec A\) and \(\vec B\) so that the resultant of these three vectors points in the negative x-direction and has a magnitude of 7.50 units?

Wähle eine der folgenden:

15.5, 209°
15.5, 151°
None of the choices.
7.5, 151°
7.5, 209°
6.12, 209°
6.12, 151°

	Erstellt von Justin Ruaya vor etwa 5 Jahre

Prepared by: Justin Ruaya Vectors, Cross Product, Dot products, Angle between Vectors, Addition, Multiplication References: Giancoli, Physics for Engineers and Scientists Wolfson, Essential Physics Fundamentals of Physics

General Physics - Vectors

General Physics - Vectors

Frage 1 von 20

We say that the displacement of a particle is a vector quantity. Our best justification for this assertion is

Wähle eine der folgenden:

Erklärung

Frage 2 von 20

Which of the following is an accurate statement?

Wähle eine der folgenden:

Erklärung

Frage 3 von 20

In the given figure, express vector \(\vec S\) in terms of \(\vec M\) and \(\vec N\).

Wähle eine der folgenden:

Erklärung

Frage 4 von 20

Check all statements that are true.

Wähle eine oder mehr der folgenden:

Erklärung

Frage 5 von 20

Which of the following diagram illustrates the relationship \(\vec c = \vec b - \vec a\)?

Wähle eine der folgenden:

Erklärung

Frage 6 von 20

The vector \(\vec V_3\) in the diagram is equal to

Wähle eine der folgenden:

Erklärung

Frage 7 von 20

Four vectors (\(\vec A, \vec B, \vec C, \vec D\)) all have the same magnitude. The angle \(\theta\) between the adjacent vectors is \(45^{\circ}\) as shown. The correct vector equation is

Wähle eine der folgenden:

Erklärung

Frage 8 von 20

Vectors \(\vec A\) and \(\vec B\) lie in the \(xy\) plane. We can deduce that \(\vec A=\vec B\) if

Wähle eine der folgenden:

Erklärung

Frage 9 von 20

If the eastward component of vector \(\vec A\) is equal to the westward component of vector \(\vec B\) and their northward components are equal. Which one of the following statements about these two vectors is correct?

Wähle eine der folgenden:

Erklärung

Frage 10 von 20

Which of the following operations will not change a vector?

Wähle eine der folgenden:

Erklärung

Frage 11 von 20

If \(\vec A\) and \(\vec B\) are nonzero vectors for which \(\vec A \cdot \vec B=0\), it must follow that

Wähle eine der folgenden:

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Frage 12 von 20

For the vectors shown in the figure, find the magnitude and direction of vector product \(\vec A \times \vec C\), assuming that the quantities shown are accurate to two significant figures.

Wähle eine der folgenden:

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Frage 13 von 20

What is the vector product of \(\vec A = 2.00 \hat i + 3.00 \hat j + 1.00 \hat k\) and \(\vec B = 1.00 \hat i - 3.00 \hat j - 2.00 \hat k\)?

Wähle eine der folgenden:

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Frage 14 von 20

What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?

Wähle eine der folgenden:

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Frage 15 von 20

Wähle eine der folgenden:

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Frage 16 von 20

Vectors A and B are shown in the figure. Vector \(\vec C\) is given by \(\vec C = \vec B -\vec A\). The magnitude of vector \(\vec A\) is 16.0 units, and the magnitude of vector \(\vec B\) is 7.00 units. What is the angle of vector \(\vec C\), measured counterclockwise from the +x-axis?

Wähle eine der folgenden:

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Frage 17 von 20

You walk 53 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

Wähle eine der folgenden:

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Frage 18 von 20

Vectors \(\vec A\) and \(\vec B\) are shown in the figure. What is \(|-5.00\vec A + 4.00 \vec B|\)?

Wähle eine der folgenden:

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Frage 19 von 20

If \(\vec A = 1.00 \hat i + 4.00 \hat j - 1.00 \hat k, \vec B = 3.00\hat i - 1.00 \hat j - 4.00 \hat k\) , and \(\vec C=-1.00\hat i + 1.00 \hat j\), then \(|(\vec A \times \vec B) \cdot \vec C|\)=?

Wähle eine der folgenden:

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Frage 20 von 20

Wähle eine der folgenden: