Q: A pilot flies 100 km east, then 100 km north. What is the magnitude of the displacement vector from the starting point?

$$\sqrt{2} \times 100\ \mathrm{km}$$

Question 1

Which of the following quantities is NOT a vector?

Accepted Answer

Speed

Question 2

A tennis racket and a set of tennis balls together cost $$110. The racket costs 100 $$more than the balls. How much do the tennis balls cost?

Accepted Answer

$5

Question 3

Which of the following is a correct notation for a vector?

Accepted Answer

$$\vec{A}$$

Question 4

Which operation is NOT valid in vector mathematics?

Accepted Answer

Adding a vector and a scalar

Question 5

If $$\vec{A}$$ and $$\vec{B}$$ are perpendicular vectors, what is their scalar (dot) product?

Accepted Answer

$$0$$

Question 6

Which of the following best describes the result of the vector cross product $$\vec{A} 	imes \vec{B}$$?

Accepted Answer

A vector

Question 7

Can two vectors of unequal magnitude ever sum to zero?

Accepted Answer

No

Question 8

Can three vectors of equal (but non-zero) magnitude ever sum to zero?

Accepted Answer

Yes

Question 9

The scalar product of two vectors $$\vec{A}$$ and $$\vec{B} is $$given by which formula?

Accepted Answer

$$A B \cos(	heta)$$

Question 10

A force of $$10\ \mathrm{N}$$ acts at an angle of $$60^\circ to $$the direction of displacement of $$5\ \mathrm{m}. $$What is the work done by the force?

Accepted Answer

$$25\ \mathrm{J}$$

Question 11

Which of the following is a scalar quantity?

Accepted Answer

Mass

Question 12

If $$\vec{A}$$ and $$\vec{B}$$ are anti-parallel vectors of equal magnitude, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

Zero vector

Question 13

Which of the following real-world examples best illustrates a vector quantity?

Accepted Answer

The velocity of a train moving north at $$80\ \mathrm{km/h}$$

Question 14

A vector $$\vec{A} is $$multiplied by a negative scalar $$-2. $$What happens to the vector?

Accepted Answer

Its magnitude is doubled and direction is reversed

Question 15

Which of the following statements about vector addition is correct?

Accepted Answer

Vector addition is commutative

Question 16

Given two vectors $$\vec{A}$$ and $$\vec{B}$$, which of the following is true about their dot product if the angle between them is $$180^\circ$$?

Accepted Answer

$$\vec{A} \cdot \vec{B} = -A B$$

Question 17

Which of the following operations will always yield a scalar?

Accepted Answer

Dot product of two vectors

Question 18

A pilot flies 100 km east, then 100 km north. What is the magnitude of the displacement vector from the starting point?

Accepted Answer

$$\sqrt{2} 	imes 100\ \mathrm{km}$$

Question 19

Which of the following best describes the physical meaning of the dot product $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

The component of $$\vec{A}$$ along $$\vec{B}$$ multiplied by the magnitude of $$\vec{B}$$

Vectors in Physics: Definitions, Operations, and Applications

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