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 𝐴 𝐵 , where 𝐴 = ( 5 , 2 ) and 𝐵 = ( 1 7 , 2 3 ) .

  • A 1 2 , 2 3
  • B 5 , 2
  • C 1 7 , 2 3
  • D 2 1 , 1 2
  • E 1 2 , 2 1

Q2:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

  • A ( 3 , 2 )
  • B ( 1 , 2 )
  • C ( 3 , 1 )
  • D ( 2 , 1 )
  • E ( 1 , 3 )

What are the coordinates of its initial point?

  • A ( 1 , 3 )
  • B ( 1 , 2 )
  • C ( 2 , 1 )
  • D ( 3 , 2 )
  • E ( 3 , 1 )

What are the components of the vector?

  • A 2 , 3
  • B 3 , 2
  • C 1 , 2
  • D 3 , 2
  • E 1 , 3

Q3:

In the given figure, 𝐴 𝐷 𝐵 𝐶 = { 𝑀 } , 𝑀 𝐴 = 𝑀 𝐷 , and 𝑀 𝐵 = 𝑀 𝐶 . Complete the following: 𝐴 𝐵 is equivalent to .

  • A 𝑀 𝐴
  • B 𝑀 𝐷
  • C 𝐶 𝐷
  • D 𝐵 𝑀

Q4:

In the given figure, 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 is a regular hexagon with center 𝑀 . Complete the following: 𝐴 𝐵 is equivalent to .

  • A 𝐹 𝑀
  • B 𝐷 𝑀
  • C 𝑀 𝐸
  • D 𝐷 𝐶
  • E 𝐵 𝑀

Q5:

Using the given figure, complete the following: | | 𝑍 𝑌 | | = and 𝑍 𝑌 = .

  • A | | 𝐵 𝐴 | | , 𝐴 𝑋
  • B | | 𝐴 𝐶 | | , 𝐵 𝐴
  • C | | 𝑋 𝐵 | | , 𝑋 𝐴
  • D | | 𝑋 𝑌 | | , 𝑋 𝑍

Q6:

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

  • A 𝑧 𝑧
  • B 𝑧 𝑧
  • C 𝑧 + 𝑧
  • D 𝑧 𝑧
  • E 𝑧 𝑧

Q7:

Given the information in the diagram below, if 𝐵 𝐶 = 𝑘 𝐸 𝐷 , find 𝑘 .

  • A 5 2
  • B 2 3
  • C 2 3
  • D 5 2

Q8:

Given the information in the diagram below, if 𝐵 𝐷 = 𝑘 𝐷 𝐴 , find 𝑘 .

  • A 3 2
  • B 2 3
  • C 3 2
  • D 2 3

Q9:

The figure shows a regular hexagon 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 divided into 6 equilateral triangles. Which of the following is equal to 𝐴 𝐹 + 𝐶 𝐷 ?

  • A 𝐴 𝐷
  • B 𝐹 𝐶
  • C 𝐸 𝐵
  • D 𝐵 𝐸
  • E 𝐹 𝐷

Q10:

Which vector is equivalent to u v + ?

  • A 𝐴 𝐶
  • B 𝐴 𝐷
  • C 𝐶 𝐵
  • D 𝐷 𝐴
  • E 𝐵 𝐶

Q11:

Which of the following diagrams is correct?

  • A
  • B
  • C
  • D
  • E

Q12:

The figure shows two vectors, v and u , where = 5 v and = 7 u . 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, v and u , are shown in the diagram.

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

Using the properties of parallelograms, find 𝜃 .

Given that v = 1 3 and u = 1 1 , use the cosine rule to find the magnitude of v u + . Give your answer to two decimal places.

Q14:

Given that | | = 3 0 A , | | = 2 8 B , and | | = 2 0 A B , determine | + | A B , rounded to two decimal places.

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