Question 1: Palette 1/10

Revision MCQ

Which one of the following statements is true concerning scalar quantities?

A

Scalar quantities must be represented by base units.

B

Scalar quantities have both magnitude and direction.

C

Scalar quantities can be added to vector quantities using rules of trigonometry.

D

Scalar quantities can be added to other scalar quantities using rules of ordinary addition.

Question 2: Palette 2/10

Revision MCQ

Which one of the following quantities is a vector quantity?

A

the age of the Earth

B

the mass of a freight train

C

the Earth's pull on your body

D

the temperature of a hot cup of coffee

Question 3: Palette 3/10

Revision MCQ

Which one of the following statements concerning vectors and scalars is false?

A

In calculations, the vector components of a vector may be used in place of the vector itself.

B

It is possible to use vector components that are not perpendicular.

C

A scalar component may be either positive or negative.

D

A vector that is zero may have components other than zero.

Question 4: Palette 4/10

Revision MCQ

Twelve coplanar forces (all of equal magnitude) maintain a body in equilibrium, then the angle between any two adjacent forces is

A

$15^\circ$

B

$30^\circ$

C

$45^\circ$

D

$60^\circ$

Question 5: Palette 5/10

Revision MCQ

If vectors $\vec{A} = \hat{i} + 2\hat{j} + 4\hat{k}$ and $\vec{B} = 5\hat{i}$ represent the two sides of a triangle, then the third side of the triangle can have length equal to

A

$6$

B

$\sqrt{56}$

C

both (a) and (b)

D

none of the above

Question 6: Palette 6/10

Revision MCQ

Mark the correct statement.

A

$\vert{}\vec{a} + \vec{b}\vert{} \ge \vert{}\vec{a}\vert{} + \vert{}\vec{b}\vert{}$

B

$\vert{}\vec{a} + \vec{b}\vert{} \le \vert{}\vec{a}\vert{} + \vert{}\vec{b}\vert{}$

C

$\vert{}\vec{a} - \vec{b}\vert{} \ge \vert{}\vec{a}\vert{} + \vert{}\vec{b}\vert{}$

D

All of the above

Question 7: Palette 7/10

Revision MCQ

Two vectors $\vec{A}$ and $\vec{B}$ are added together to form the vector $\vec{C} = \vec{A} + \vec{B}$. The relationship between the components of these vectors is given by $C_x = A\cos 30^\circ + B$ and $C_y = -A\sin 30^\circ$. Which statement best describes the orientation of these vectors?

A

Vector $\vec{A}$ makes an angle of $30^\circ$ below the positive x-axis, and vector $\vec{B}$ points along the positive x-axis.

B

Vector $\vec{A}$ points in the negative x-direction, while vector $\vec{B}$ points in the positive y-direction.

C

Vector $\vec{A}$ points in the negative y-direction, while vector $\vec{B}$ points in the positive x-direction.

D

Vector $\vec{A}$ makes an angle of $30^\circ$ above the positive x-axis, and vector $\vec{B}$ points along the negative x-axis.

Question 8: Palette 8/10

Revision MCQ

Three vectors $\vec{A}$, $\vec{B}$, and $\vec{C}$ add together to yield zero: $\vec{A} + \vec{B} + \vec{C} = 0$. The vectors $\vec{A}$ and $\vec{C}$ point in opposite directions and their magnitudes are related by the expression: $A = 2C$. Which one of the following conclusions is correct?

A

$\vec{A}$ and $\vec{B}$ have equal magnitudes and point in opposite directions.

B

$\vec{B}$ and $\vec{C}$ have equal magnitudes and point in the same direction.

C

$\vec{B}$ and $\vec{C}$ have equal magnitudes and point in opposite directions.

D

$\vec{A}$ and $\vec{B}$ point in the same direction, but $A$ has twice the magnitude of $B$.

Question 9: Palette 9/10

Revision MCQ

Given that $\vec{A} + 2\vec{B} = x_1\hat{i} + y_1\hat{j}$ and $2\vec{A} - \vec{B} = x_2\hat{i} + y_2\hat{j}$, what is $\vec{A}$?

A

$\vec{A} = \frac{1}{5}(x_1 + 2x_2)\hat{i} + \frac{1}{5}(y_1 + 2y_2)\hat{j}$

B

$\vec{A} = \frac{1}{5}(x_1 + 2x_2)\hat{i} - \frac{1}{5}(y_1 + 2y_2)\hat{j}$

C

$\vec{A} = \frac{1}{5}(x_1 + 4x_2)\hat{i} + \frac{1}{5}(y_1 + 2y_2)\hat{j}$

D

$\vec{A} = \frac{1}{5}(x_1 + 4x_2)\hat{i} + \frac{1}{5}(y_1 + 4y_2)\hat{j}$

Question 10: Palette 10/10

Revision MCQ

The vector $\vec{A}$ has components $+5$ and $+7$ along the $x$-axes and $y$-axes, respectively. Along a set of axes rotated $90^\circ$ degrees counterclockwise relative to the original axes, the vector's components are

A

$-7; -5$

B

$7; -5$

C

$-7; 5$

D

$7; 5$