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 𝐴𝐵, where 𝐴=(5,2) and 𝐵=(17,23).

  • A5,2
  • B12,23
  • C21,12
  • D12,21
  • E17,23

Q2:

Consider the vector in the given diagram.

What are the coordinates of its terminal point?

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

What are the coordinates of its initial point?

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

What are the components of the vector?

  • A2,3
  • B1,2
  • C3,2
  • D1,3
  • E3,2

Q3:

In the given figure, 𝐴𝐷𝐵𝐶={𝑀}, 𝑀𝐴=𝑀𝐷, and 𝑀𝐵=𝑀𝐶. Complete the following: 𝐴𝐵 is equivalent to .

  • A𝑀𝐷
  • B𝐶𝐷
  • C𝑀𝐴
  • D𝐵𝑀

Q4:

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

  • A𝑀𝐸
  • B𝐹𝑀
  • C𝐵𝑀
  • D𝐷𝐶
  • E𝐷𝑀

Q5:

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

  • A||𝑋𝑌||, 𝑋𝑍
  • B||𝑋𝐵||, 𝑋𝐴
  • C||𝐴𝐶||, 𝐵𝐴
  • D||𝐵𝐴||, 𝐴𝑋

Q6:

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

  • A𝑧𝑧
  • B𝑧𝑧
  • C𝑧𝑧
  • D𝑧𝑧
  • E𝑧+𝑧

Q7:

Given the information in the diagram below, if 𝐵𝐶=𝑘𝐸𝐷, find 𝑘.

  • A52
  • B52
  • C23
  • D23

Q8:

Given the information in the diagram below, if 𝐵𝐷=𝑘𝐷𝐴, find 𝑘.

  • A32
  • B23
  • C32
  • D23

Q9:

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

  • A𝐸𝐵
  • B𝐵𝐸
  • C𝐹𝐷
  • D𝐴𝐷
  • E𝐹𝐶

Q10:

Which vector is equivalent to uv+?

  • A𝐴𝐷
  • B𝐶𝐵
  • C𝐷𝐴
  • D𝐴𝐶
  • E𝐵𝐶

Q11:

Which of the following diagrams is correct?

  • A
  • B
  • C
  • D
  • E

Q12:

The figure shows two vectors, v and u, where =5v and =7u. 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=13 and u=11, use the cosine rule to find the magnitude of vu+. Give your answer to two decimal places.

Q14:

Given that ||=30A, ||=28B, and ||=20AB, determine |+|AB, rounded to two decimal places.

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