General Physics - Vectors

Question 1 of 20

1

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

Select one of the following:

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

Explanation

Question 2 of 20

1

Which of the following is an accurate statement?

Select one of the following:

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.

Explanation

Question 3 of 20

1

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

Select one of the following:

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

Explanation

Question 4 of 20

3

Check all statements that are true.

Select one or more of the following:

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.

Explanation

Question 5 of 20

1

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

Select one of the following:

Explanation

Question 6 of 20

1

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

Select one of the following:

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

Explanation

Question 7 of 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

Select one of the following:

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

Explanation

Question 8 of 20

1

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

Select one of the following:

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

Explanation

Question 9 of 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?

Select one of the following:

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.

Explanation

Question 10 of 20

1

Which of the following operations will not change a vector?

Select one of the following:

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.

Explanation

Question 11 of 20

1

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

Select one of the following:

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

Explanation

Question 12 of 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.

Select one of the following:

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

Explanation

Question 13 of 20

2

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

Select one of the following:

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

Explanation

Question 14 of 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?

Select one of the following:

6.93
-6.93
4.00
-4.00
8.00
6.81

Explanation

Question 15 of 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?

Select one of the following:

2.5N
5.1N
6.0N
7.8N

Explanation

Question 16 of 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?

Select one of the following:

16.9°
22.4°
73.1°
287°
292°
68

Explanation

Question 17 of 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.

Select one of the following:

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

Explanation

Question 18 of 20

3

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

Select one of the following:

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

Explanation

Question 19 of 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 \(|(\vec A \times \vec B) \cdot \vec C|\)=?

Select one of the following:

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

Explanation

Question 20 of 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?

Select one of the following:

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

	Created by Justin Ruaya about 5 years ago

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

Question 1 of 20

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

Select one of the following:

Explanation

Question 2 of 20

Which of the following is an accurate statement?

Select one of the following:

Explanation

Question 3 of 20

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

Select one of the following:

Explanation

Question 4 of 20

Check all statements that are true.

Select one or more of the following:

Explanation

Question 5 of 20

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

Select one of the following:

Explanation

Question 6 of 20

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

Select one of the following:

Explanation

Question 7 of 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

Select one of the following:

Explanation

Question 8 of 20

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

Select one of the following:

Explanation

Question 9 of 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?

Select one of the following:

Explanation

Question 10 of 20

Which of the following operations will not change a vector?

Select one of the following:

Explanation

Question 11 of 20

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

Select one of the following:

Explanation

Question 12 of 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.

Select one of the following:

Explanation

Question 13 of 20

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

Select one of the following:

Explanation

Question 14 of 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?

Select one of the following:

Explanation

Question 15 of 20

Select one of the following:

Explanation

Question 16 of 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?

Select one of the following:

Explanation

Question 17 of 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.

Select one of the following:

Explanation

Question 18 of 20

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

Select one of the following:

Explanation

Question 19 of 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 \(|(\vec A \times \vec B) \cdot \vec C|\)=?

Select one of the following:

Explanation

Question 20 of 20

Select one of the following:

Explanation