# Worksheet: Graphical Operations on Vectors

In this worksheet, we will practice doing operations on vectors graphically such as addition, subtraction and scalar multiplication using triangle and parallelogram rules.

Q1:

Find the components of the vector , where and .

• A
• B
• C
• D
• E

Q2:

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?

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• B
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• D
• E

What are the components of the vector?

• A
• B
• C
• D
• E

Q3:

In the given figure, , , and . Complete the following: is equivalent to .

• A
• B
• C
• D

Q4:

In the given figure, is a regular hexagon with center . Complete the following: is equivalent to .

• A
• B
• C
• D
• E

Q5:

Using the given figure, complete the following: and .

• A,
• B,
• C,
• D,

Q6:

The blue vector represents the complex number . The green vector represents the vector . What does the red vector represent?

• A
• B
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• E

Q7:

Given the information in the diagram below, if , find .

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• B
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• D

Q8:

Given the information in the diagram below, if , find .

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• B
• C
• D

Q9:

The figure shows a regular hexagon divided into 6 equilateral triangles. Which of the following is equal to ?

• A
• B
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• D
• E

Q10:

Which vector is equivalent to ?

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• D
• E

Q11:

Which of the following diagrams is correct?

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• D
• E

Q12:

The figure shows two vectors, and , where and . Use the parallelogram method to find the magnitude of the resultant of these two vectors. Give your answer to two decimal places.

Q13:

The two vectors, and , are shown in the diagram.

The following parallelogram is drawn based on the two vectors and .

Using the properties of parallelograms, find .

Given that and , use the cosine rule to find the magnitude of . Give your answer to two decimal places.

Q14:

Given that , , and , determine , rounded to two decimal places.

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