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 \(\vec c = \vec b - \vec a\)?
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
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.
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?
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?
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 \(|-5.00\vec A + 4.00 \vec B|\)?
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?