General Physics - Vectors

Justin Ruaya
Quiz by Justin Ruaya, updated more than 1 year ago
Justin Ruaya
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
Answer
  • 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?
Answer
  • 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 \(\vec N\).
Answer
  • \[\vec S = -\vec M - \vec N\]
  • \[\vec S = \vec N - \vec M\]
  • \[\vec S = \vec M + \vec N\]
  • \[\vec S = \vec M - \vec N\]

Question 4

Question
Check all statements that are true.
Answer
  • 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
Answer
  • \(\vec V_1 - \vec V_2\)
  • \(\vec V_1 + \vec V_2\)
  • \(\vec V_2 - \vec V_1\)
  • \(\vec V_1 \cos \theta \)
  • \(\vec V_1 / (\cos \theta)\)

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

Question 8

Question
Vectors \(\vec A\) and \(\vec B\) lie in the \(xy\) plane. We can deduce that \(\vec A=\vec B\) if
Answer
  • \({A^2}_x+{A^2}_y={B^2}_x+{B^2}_y\)
  • \(A_x+A_y=B_x+B_y\)
  • \(A_x=B_x\) 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?
Answer
  • 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?
Answer
  • 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
Answer
  • \(\vec A \times \vec B=0\)
  • \(\vec A\) 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.
Answer
  • 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 \(\vec B = 1.00 \hat i - 3.00 \hat j - 2.00 \hat k\)?
Answer
  • \(-3.00 \hat i + 5.00 \hat j - 9.00 \hat k\)
  • \(-5.00 \hat i + 2.00 \hat j - 6.00 \hat k\)
  • \(5\)
  • \(2.00 \hat i -9.00 \hat j - 2.00 \hat k\)
  • \(-9\)

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?
Answer
  • 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?
Answer
  • 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?
Answer
  • 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.
Answer
  • 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 \(|-5.00\vec A + 4.00 \vec B|\)?
Answer
  • 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 \(|(\vec A \times \vec B) \cdot \vec C|\)=?
Answer
  • 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?
Answer
  • 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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