Q: When adding two vectors $\\vec{A}$ and $\\vec{B}$ using the parallelogram method, what does the diagonal of the parallelogram represent?

The resultant vector $\\vec{A} + \\vec{B}$

Q: Which statement is TRUE about vector addition?

Vector addition is commutative: $\\vec{A} + \\vec{B} = \\vec{B} + \\vec{A}$

Q: A vector $\\vec{A}$ is multiplied by a scalar $c = -2$. What is the result?

A vector in the opposite direction to $\\vec{A}$ with magnitude $2A$

Q: A vector $\\vec{A}$ makes an angle $\\theta$ with the positive x-axis. What are its components?

$A_x = A \\cos \\theta, A_y = A \\sin \\theta$

Q: A rescue helicopter flies $100\ \mathrm{m}$ east, then $50\ \mathrm{m}$ north. What is the magnitude of its displacement from the starting point?

$\\sqrt{100^2 + 50^2} = 111.8\ \mathrm{m}$

Q: If $\\vec{A}$ has components $A_x = 6$, $A_y = 8$, what is the direction angle $\\theta$ with respect to the positive x-axis?

$\\theta = \\arctan(8/6) = 53.1^\\circ$

Question 1

Which of the following is a scalar quantity?

Accepted Answer

Temperature

Question 2

A car moves $50.0\ \mathrm{m}$ at an angle of $37^\circ$ south of west. Which method can be used to graphically add this displacement to another vector?

Accepted Answer

Tip-to-tail method

Question 3

When adding two vectors $\vec{A}$ and $\vec{B}$ using the parallelogram method, what does the diagonal of the parallelogram represent?

Accepted Answer

The resultant vector $\vec{A} + \vec{B}$

Question 4

If $\vec{A}$ has components $A_x = 3$ and $A_y = 4$, what is the magnitude of $\vec{A}$?

Accepted Answer

$\sqrt{3^2 + 4^2} = 5$

Question 5

Which statement is TRUE about vector addition?

Accepted Answer

Vector addition is commutative: $\vec{A} + \vec{B} = \vec{B} + \vec{A}$

Question 6

A vector $\vec{A}$ is multiplied by a scalar $c = -2$. What is the result?

Accepted Answer

A vector in the opposite direction to $\vec{A}$ with magnitude $2A$

Question 7

Given two vectors $\vec{A}$ and $\vec{B}$ with components $A_x = 2$, $A_y = 5$, $B_x = -1$, $B_y = 3$, what are the components of $\vec{C} = \vec{A} + \vec{B}$?

Accepted Answer

$C_x = 1, C_y = 8$

Question 8

Which of the following best describes the difference between a scalar and a vector?

Accepted Answer

A scalar has only magnitude; a vector has magnitude and direction

Question 9

A vector $\vec{A}$ makes an angle $\theta$ with the positive x-axis. What are its components?

Accepted Answer

$A_x = A \cos \theta, A_y = A \sin \theta$

Question 10

If $\vec{A}$ and $\vec{B}$ are two vectors, which equation correctly represents their difference using components?

Accepted Answer

$C_x = A_x - B_x, C_y = A_y - B_y$

Question 11

A rescue helicopter flies $100\ \mathrm{m}$ east, then $50\ \mathrm{m}$ north. What is the magnitude of its displacement from the starting point?

Accepted Answer

$\sqrt{100^2 + 50^2} = 111.8\ \mathrm{m}$

Question 12

Which of the following is NOT a valid way to represent a vector?

Accepted Answer

Using non-bold, italic letters (e.g., $m$)

Question 13

A vector $\vec{A}$ is multiplied by a scalar $c = 0$. What is the result?

Accepted Answer

A vector with zero magnitude

Question 14

Which real-world scenario best illustrates the concept of vector subtraction?

Accepted Answer

Finding the change in velocity of a car after braking

Question 15

If $\vec{A}$ has components $A_x = 6$, $A_y = 8$, what is the direction angle $\theta$ with respect to the positive x-axis?

Accepted Answer

$\theta = \arctan(8/6) = 53.1^\circ$

Question 16

A vector $\vec{B}$ has magnitude $10$ and points $60^\circ$ above the x-axis. What is $B_x$?

Accepted Answer

$B_x = 10 \cos 60^\circ = 5.0$

Question 17

Which operation is required to find the component of a vector along the y-axis?

Accepted Answer

Multiply the magnitude by $\sin \theta$

Question 18

A boat travels $4\ \mathrm{km}$ east and then $3\ \mathrm{km}$ north. What is the direction of its displacement from the starting point?

Accepted Answer

$\theta = \arctan(3/4) = 36.9^\circ$ north of east

Vectors and Scalars: Concepts and Operations in Physics

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