General Physics - Vectors

Question 1

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

Accepted Answer

operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments

Answer

displacement can be specified by a magnitude and a direction

Answer

a displacement is obviously not a scalar

Answer

displacement can be specified by three numbers

Answer

displacement is associated with motion, where velocity is a vector

Question 2

Which of the following is an accurate statement?

Accepted Answer

A vector cannot have zero magnitude if one of its components is not zero

Answer

The magnitude of a vector can be less than the magnitude of one of its components.

Answer

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.

Answer

The magnitude of a vector can be positive or negative.

Question 3

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

Accepted Answer

$$\vec S = \vec M - \vec N$$

Answer

$$\vec S = -\vec M - \vec N$$

Answer

$$\vec S = \vec N - \vec M$$

Answer

$$\vec S = \vec M + \vec N$$

Question 4

Check all statements that are true.

Accepted Answer

The magnitude of a vector can never be less than the magnitude of one of its components

Accepted Answer

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.

Accepted Answer

If two vectors point in opposite directions, their cross product must be zero.

Answer

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 $\vec B$.

Answer

If all the components of a vector are equal to 1, then that vector is a unit vector.

Answer

If two vectors are perpendicular to each other, their dot product must be zero.

Question 5

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

Question 6

The vector $\vec V_3$ in the diagram is equal to

Accepted Answer

$\vec V_2 - \vec V_1$

Answer

$\vec V_1 - \vec V_2$

Answer

$\vec V_1 + \vec V_2$

Answer

$\vec V_1 \cos \theta $

Answer

$\vec V_1 / (\cos \theta)$

Question 7

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

Accepted Answer

$\vec B + \vec D - \sqrt{2}\vec C=0$

Answer

$\vec A - \vec B - \vec C + \vec D = 0$

Answer

$\vec A + \vec B = \vec B + \vec D$

Answer

$\vec A + \vec B + \vec C + \vec D = 0$

Answer

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

Question 8

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

Accepted Answer

$A_x=B_x$ and $A_y=B_y$

Answer

${A^2}_x+{A^2}_y={B^2}_x+{B^2}_y$

Answer

$A_x+A_y=B_x+B_y$

Answer

$\frac{A_y}{A_x}=\frac{B_x}{B_y}$

Answer

$A_x=B_y$ and $A_y=B_x$

Question 9

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?

Accepted Answer

The magnitude of vector $\vec A$ is equal to the magnitude of $\vec B$.

Answer

Vector $\vec A$ is parallel to vector $\vec B$

Answer

Vectors $\vec A$ and $\vec B$ point in opposite directions.

Answer

Vector $\vec A$ is perpendicular to vector $\vec B$

Answer

None of the statements.

Question 10

Which of the following operations will not change a vector?

Accepted Answer

Translate it parallel to itself.

Answer

Rotate it

Answer

Multiply it by a constant factor.

Answer

Add a constant vector to it.

Answer

Translate it perpendicular to itself.

Answer

None of the choices.

Question 11

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

Accepted Answer

$|\vec A \times \vec B|=AB$

Answer

$\vec A \times \vec B=0$

Answer

$\vec A$ is parallel to $\vec B$.

Answer

$|\vec A \times \vec B|=1$

Answer

None of the statements.

Question 12

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.

Accepted Answer

45, directed out of the plane

Answer

16, directed into the plane

Answer

16, directed out of the plane

Answer

45, directed into the plane

Question 13

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

Accepted Answer

$-3.00 \hat i + 5.00 \hat j - 9.00 \hat k$

Answer

$-5.00 \hat i + 2.00 \hat j - 6.00 \hat k$

Answer

$5$

Answer

$2.00 \hat i -9.00 \hat j - 2.00 \hat k$

Answer

$-9$

Question 14

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?

Accepted Answer

6.93

Answer

-6.93

Answer

4.00

Answer

-4.00

Answer

8.00

Answer

6.81

Question 15

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?

Accepted Answer

2.5N

Answer

5.1N

Answer

6.0N

Answer

7.8N

Question 16

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?

Accepted Answer

292°

Answer

16.9°

Answer

22.4°

Answer

73.1°

Answer

287°

Answer

68

Question 17

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.

Accepted Answer

63° N of E

Answer

50° N of E

Answer

57° N of E

Answer

69° N of E

Question 18

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

Accepted Answer

31.8

Answer

$-32.0 \hat i - 2.00 \hat k$

Answer

1028

Answer

34

Answer

$-2.00\hat i - 32.0 \hat j$

Question 19

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 $|(\vec A \times \vec B) \cdot \vec C|$=?

Accepted Answer

18

Answer

$12.00 \hat i - 6.00 \hat j - 12\hat k$

Answer

$-3.00\hat i -4.00 \hat j-4.00\hat k$

Answer

$6.00 \hat i - 12.00 \hat j - 12\hat k$

Answer

$12\sqrt{3}$

Answer

-7

Answer

7

Question 20

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?

Accepted Answer

15.5, 209°

Answer

15.5, 151°

Answer

None of the choices.

Answer

7.5, 151°

Answer

7.5, 209°

Answer

6.12, 209°

Answer

6.12, 151°

General Physics - Vectors

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