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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