# General Physics - Vectors

Quiz by Justin Ruaya, updated more than 1 year ago
 Created by Justin Ruaya about 2 years ago
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### Description

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

## Resource summary

### Question 1

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

### Question 2

Question
Which of the following is an accurate statement?
• 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.

### Question 3

Question
In the given figure, express vector $$\vec S$$ in terms of $$\vec M$$ and $$\vec N$$.
• $\vec S = -\vec M - \vec N$
• $\vec S = \vec N - \vec M$
• $\vec S = \vec M + \vec N$
• $\vec S = \vec M - \vec N$

### Question 4

Question
Check all statements that are true.
• 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.

### Question 5

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

### Question 6

Question
The vector $$\vec V_3$$ in the diagram is equal to
• $$\vec V_1 - \vec V_2$$
• $$\vec V_1 + \vec V_2$$
• $$\vec V_2 - \vec V_1$$
• $$\vec V_1 \cos \theta$$
• $$\vec V_1 / (\cos \theta)$$

### Question 7

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

### Question 8

Question
Vectors $$\vec A$$ and $$\vec B$$ lie in the $$xy$$ plane. We can deduce that $$\vec A=\vec B$$ if
• $${A^2}_x+{A^2}_y={B^2}_x+{B^2}_y$$
• $$A_x+A_y=B_x+B_y$$
• $$A_x=B_x$$ and $$A_y=B_y$$
• $$\frac{A_y}{A_x}=\frac{B_x}{B_y}$$
• $$A_x=B_y$$ and $$A_y=B_x$$

### Question 9

Question
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?
• 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.

### Question 10

Question
Which of the following operations will not change a vector?
• 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.

### Question 11

Question
If $$\vec A$$ and $$\vec B$$ are nonzero vectors for which $$\vec A \cdot \vec B=0$$, it must follow that
• $$\vec A \times \vec B=0$$
• $$\vec A$$ is parallel to $$\vec B$$.
• $$|\vec A \times \vec B|=AB$$
• $$|\vec A \times \vec B|=1$$
• None of the statements.

### Question 12

Question
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.
• 16, directed into the plane
• 16, directed out of the plane
• 45, directed into the plane
• 45, directed out of the plane

### Question 13

Question
What is the vector product of $$\vec A = 2.00 \hat i + 3.00 \hat j + 1.00 \hat k$$ and $$\vec B = 1.00 \hat i - 3.00 \hat j - 2.00 \hat k$$?
• $$-3.00 \hat i + 5.00 \hat j - 9.00 \hat k$$
• $$-5.00 \hat i + 2.00 \hat j - 6.00 \hat k$$
• $$5$$
• $$2.00 \hat i -9.00 \hat j - 2.00 \hat k$$
• $$-9$$

### Question 14

Question
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?
• 6.93
• -6.93
• 4.00
• -4.00
• 8.00
• 6.81

### Question 15

Question
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?
• 2.5N
• 5.1N
• 6.0N
• 7.8N

### Question 16

Question
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?
• 16.9°
• 22.4°
• 73.1°
• 287°
• 292°
• 68

### Question 17

Question
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.
• 63° N of E
• 50° N of E
• 57° N of E
• 69° N of E

### Question 18

Question
Vectors $$\vec A$$ and $$\vec B$$ are shown in the figure. What is $$|-5.00\vec A + 4.00 \vec B|$$?
• 31.8
• $$-32.0 \hat i - 2.00 \hat k$$
• 1028
• 34
• $$-2.00\hat i - 32.0 \hat j$$

### Question 19

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

### Question 20

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

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