Vectors: Introduction of vectors

Question 1

What is a vector?

Answer 1

A vector quantity has both magnitude (size) and direction.

Question 2

What is a scalar?

Answer 2

A scalar quantity has magnitude only.

Question 3

How is the angle theta measured?

Answer 3

The angle,
theta, is measured in an anticlockwise direction from the positive x-axis.

Question 4

What is r?

Answer 4

r is the magnitude (size) of the vector.

Question 5

What is this in magnitude-direction form?

Answer 5

The diagram shows the vector (5, 53.1°)

Question 6

What are the unit vectors i and j?

Answer 6

i is a unit vector in the x direction.
j is a unit vector in the y direction.

Question 7

What is this diagram in unit vectors?

Answer 7

The vector, a, is 3i + 4j or (3,4)

Question 8

How is the magnitude, |c|, calculated?

Answer 8

Question 9

How can a vector given in magnitude-direction form can be written in component form?

Answer 9

Question 10

Answer 10

Question 11

Answer 11

Question 12

How do you multiply a vector with a scalar?

Answer 12

Question 13

Answer 13

Question 14

Answer 14

Question 15

Answer 15

Question 16

How are two vectors equal?

Answer 16

Two vectors are equal if they have the same magnitude and direction.

Question 17

Answer 17

Question 18

Answer 18

Question 19

What is a unit vector’s magnitude?

Answer 19

A unit vector has a magnitude of 1.

Question 20

What is the unit vector written as?

Answer 20

Question 21

Answer 21