# Worksheet: Component Form of a Vector

In this worksheet, we will practice expressing a vector in component form given its initial and terminal points.

Q1:

Find the components of the vector , where and .

• A
• B
• C
• D
• E

Q2:

Find the coordinates of the terminal point of the vector in the given diagram.

• A
• B
• C
• D
• E

Q3:

Find the coordinates of the initial point of the vector in the given diagram.

• A
• B
• C
• D
• E

Q4:

Find the components of the vector , where and .

• A
• B
• C
• D
• E

Q5:

A vector has components and a terminal point . What is its initial point?

• A
• B
• C
• D
• E

Q6:

Find the components of the vector .

• A
• B
• C
• D
• E

Q7:

The initial point of the vector shown in the diagram is the origin, .

What are the coordinates of its terminal point?

• A
• B
• C
• D
• E

What are the components of the vector?

• A
• B
• C
• D
• E

Q8:

The initial point of the vector shown in the diagram is the origin, .

What are the coordinates of its terminal point?

• A
• B
• C
• D
• E

What are the components of the vector?

• A
• B
• C
• D
• E

Q9:

The initial point of the vector shown in the diagram is the origin, .

What are the coordinates of its terminal point?

• A
• B
• C
• D
• E

What are the components of the vector?

• A
• B
• C
• D
• E

Q10:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

• A
• B
• C
• D
• E

What are the coordinates of its initial point?

• A
• B
• C
• D
• E

What are the components of the vector?

• A
• B
• C
• D
• E

Q11:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

• A
• B
• C
• D
• E

What are the coordinates of its initial point?

• A
• B
• C
• D
• E

What are the components of the vector?

• A
• B
• C
• D
• E

Q12:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

• A
• B
• C
• D
• E

What are the coordinates of its initial point?

• A
• B
• C
• D
• E

What are the components of the vector?

• A
• B
• C
• D
• E

Q13:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

• A
• B
• C
• D
• E

What are the coordinates of its initial point?

• A
• B
• C
• D
• E

What are the components of the vector?

• A
• B
• C
• D
• E

Q14:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

• A
• B
• C
• D
• E

What are the coordinates of its initial point?

• A
• B
• C
• D
• E

What are the components of the vector?

• A
• B
• C
• D
• E

Q15:

Suppose the coordinates of points and are and respectively. Find the components of the vector in terms of , , , and .

• A
• B
• C
• D
• E

Q16:

A vector has components and an initial point . What is its terminal point?

• A
• B
• C
• D
• E

Q17:

Find the components of the vector , where and .

• A
• B
• C
• D
• E

Q18:

Find the components of the vector .

• A
• B
• C
• D
• E

Q19:

Given that the coordinates of and are and respectively, find .

Q20:

Find the components of the vector , where and .

• A
• B
• C
• D
• E

Q21:

What is the magnitude of the vector , where and ?

Q22:

Using the shown graph, determine the position vector of point relative to the origin point , denoted by , and find its norm, denoted by .

• A ,
• B ,
• C ,
• D ,
• E ,

Q23:

What is the initial point of the vector in the given diagram?

• A
• B

Q24:

What is the terminal point of the vector in the given diagram?

• A
• B

Q25:

The points , , and have coordinates , , and respectively. Given that and are equivalent vectors, find the coordinates of .

• A
• B
• C
• D
• E