Question 1

Which of the following statements best describes a vector?

Accepted Answer

A quantity that has both magnitude and direction.

Question 2

If a particle's velocity vector is $$\vec{v}$$ and its magnitude is $$v = 5\ \mathrm{m/s}$$, what does the magnitude represent?

Accepted Answer

The speed of the particle.

Question 3

Two vectors $$\vec{d}_B$$ and $$\vec{d}_S$$ have the same magnitude and direction but start at different points. Which of the following is true?

Accepted Answer

They are equal because vectors are defined by magnitude and direction only.

Question 4

A hiker walks 4 miles east and then 3 miles north. What is the magnitude of the net displacement?

Accepted Answer

$$5\ \mathrm{mi}$$

Question 5

Which rule states that to add two vectors, you place the tail of the second vector at the tip of the first vector?

Accepted Answer

Tip-to-tail rule

Question 6

If $$\vec{A}$$ and $$\vec{B}$$ are vectors, which equation correctly represents their sum?

Accepted Answer

$$\vec{A} + \vec{B} = \vec{B} + \vec{A}$$

Question 7

Multiplying a vector $$\vec{A} by a $$positive scalar $$c$$ results in:

Accepted Answer

A vector with magnitude $$cA in $$the same direction as $$\vec{A}.$$

Question 8

What happens when a vector $$\vec{A} is $$multiplied by $$-1$$?

Accepted Answer

Its direction is reversed but magnitude remains the same.

Question 9

Which of the following is the correct way to subtract vector $$\vec{B}$$ from $$\vec{A}$$?

Accepted Answer

Add $$\vec{A}$$ and $$-\vec{B}$$: $$\vec{A} + (-\vec{B})$$

Question 10

A vector cannot have which of the following properties?

Accepted Answer

A negative magnitude

Question 11

If $$\vec{A} is a $$vector and $$c is a $$scalar, which equation shows the result of multiplying $$\vec{A} by$$ $$c$$?

Accepted Answer

$$\vec{B} = c\vec{A}$$

Question 12

A car travels 6 km north, then 8 km east. What is the magnitude of its net displacement?

Accepted Answer

$$10\ \mathrm{km}$$

Question 13

Which of the following best describes the zero vector?

Accepted Answer

A vector with zero magnitude and no direction.

Question 14

If $$\vec{A}$$ and $$\vec{B}$$ are perpendicular and $$|\vec{A}| = 3$$, $$|\vec{B}| = 4$$, what is $$|\vec{A} + \vec{B}|$$?

Accepted Answer

$$5$$

Question 15

Which of the following is true about vector addition?

Accepted Answer

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

Question 16

A vector $$\vec{A} is $$multiplied by $$-3. $$Which statement is correct?

Accepted Answer

The new vector has magnitude $$3A$$ and points in the opposite direction.

Question 17

Which of the following is a correct statement about the magnitude of a vector?

Accepted Answer

It can never be negative.

Question 18

A vector $$\vec{A} is $$added to its negative $$-\vec{A}. $$What is the result?

Accepted Answer

The zero vector $$\vec{0}$$

Question 19

Which of the following best describes the parallelogram rule for vector addition?

Accepted Answer

The diagonal of the parallelogram formed by two vectors represents their sum.

Vectors: Definitions, Properties, and Operations

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