General Physics - Vectors

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

Which of the following is an accurate statement?

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

Check all statements that are true.

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

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

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

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?

Which of the following operations will not change a vector?

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

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 \(\vec B = 1.00 \hat i - 3.00 \hat j - 2.00 \hat k\)?

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?

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.

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

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?