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Worksheet: Graphical Operations on Vectors

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?

  • A
  • B
  • C
  • D
  • E

What are the components of the vector?

  • A
  • B
  • C
  • D
  • E

Q3:

In the given figure, 𝐴 𝐷 ∩ 𝐡 𝐢 = { 𝑀 } , 𝑀 𝐴 = 𝑀 𝐷 , and 𝑀 𝐡 = 𝑀 𝐢 . Complete the following: οƒ  𝐴 𝐡 is equivalent to .

  • A οƒ  𝑀 𝐷
  • B οƒ  𝑀 𝐴
  • C οƒ  𝐡 𝑀
  • D οƒ  𝐢 𝐷

Q4:

In the given figure, 𝐴 𝐡 𝐢 𝐷 𝐸 𝐹 is a regular hexagon with centre 𝑀 . Complete the following: οƒ  𝐴 𝐡 is equivalent to .

  • A οƒ  𝐷 𝑀
  • B οƒ  𝑀 𝐸
  • C οƒ  𝐷 𝐢
  • D οƒ  𝐹 𝑀
  • E οƒ  𝐡 𝑀

Q5:

Using the given figure, complete the following: | | οƒ  𝑍 π‘Œ | | = and οƒ  𝑍 π‘Œ = .

  • A | | οƒ  𝐴 𝐢 | | , οƒ  𝐡 𝐴
  • B | | οƒ  𝐡 𝐴 | | , οƒ  𝐴 𝑋
  • C | | οƒ  𝑋 π‘Œ | | , οƒ  𝑋 𝑍
  • D | | οƒ  𝑋 𝐡 | | , οƒ  𝑋 𝐴

Q6:

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

  • A 𝑧 βˆ’ 𝑧  
  • B 𝑧 𝑧  
  • C 𝑧 𝑧  
  • D 𝑧 + 𝑧  
  • E 𝑧 𝑧  

Q7:

Given the information in the diagram below, if οƒŸ 𝐡 𝐢 = π‘˜ οƒ  𝐸 𝐷 , find π‘˜ .

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

Q8:

Given the information in the diagram below, if οƒ  𝐡 𝐷 = π‘˜ οƒ  𝐷 𝐴 , find π‘˜ .

  • A βˆ’ 2 3
  • B 3 2
  • C βˆ’ 3 2
  • D 2 3