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Worksheet: Vector Operations

Q1:

Given that and , find .

  • A
  • B
  • C
  • D

Q2:

Given that and , find .

  • A
  • B
  • C
  • D

Q3:

Given that and , find .

  • A
  • B
  • C
  • D

Q4:

Given that and , find .

  • A
  • B
  • C
  • D

Q5:

Given that and , find .

  • A
  • B
  • C
  • D

Q6:

Given that and , find .

  • A
  • B
  • C
  • D

Q7:

Given that and , find .

  • A
  • B
  • C
  • D

Q8:

Given that and , find .

  • A
  • B
  • C
  • D

Q9:

Given that and , find .

  • A
  • B
  • C
  • D

Q10:

Given that and , find .

  • A
  • B
  • C
  • D

Q11:

Given that and , find .

  • A
  • B
  • C
  • D

Q12:

Given that and , find .

  • A
  • B
  • C
  • D

Q13:

On a lattice, where , , and , determine the coordinates of the point .

  • A
  • B
  • C
  • D

Q14:

Given that u = 0 , 4 and v = 0 , 5 , find the components of u v + .

  • A 0 , 2 0
  • B 0 , 9
  • C 5 , 4
  • D 0 , 1
  • E 0 , 1

Q15:

A force of ( + + ) i j k newtons is being applied to an object. What other force should be applied to achieve a total force of ( 2 + + ) i j k newtons?

  • A ( + 2 + 2 ) i j k newtons
  • B 3 i newtons
  • C ( 2 2 ) i j k newtons
  • D 3 i newtons
  • E ( 3 + + ) i j k newtons

Q16:

Given that u = 2 , 3 , v = 5 , 4 , and w = 3 , 1 , find the components of u v w + + .

  • A 1 5 , 1 2
  • B 3 , 1
  • C 4 , 6
  • D 0 , 0
  • E 0 , 2

Q17:

Given that u = 2 , 3 , v = 3 , 2 , and w = 1 , 5 , find the components of u v w + + .

  • A 6 , 3 0
  • B 5 , 1
  • C 0 , 0
  • D 4 , 6
  • E 6 , 4

Q18:

Given that u = 2 , 4 and v = 0 , 0 , find the components of u v + .

  • A 2 , 4
  • B 0 , 0
  • C 4 , 2
  • D 2 , 4
  • E 4 , 2

Q19:

and Find ( + ) A B A .

Q20:

Shown on the grid of unit squares are the vectors u , v , and u v + .

What are the components of u ?

  • A 4 , 2
  • B 4 , 1
  • C 5 , 1
  • D 4 , 1
  • E 5 , 2

What are the components of v ?

  • A 5 , 1
  • B 6 , 1
  • C 5 , 2
  • D 5 , 1
  • E 6 , 1

What are the components of u v + ?

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

Q21:

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

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

Q22:

Given that u = 2 , 4 and v = 2 , 4 , find the components of u v + .

  • A 4 , 8
  • B 4 , 8
  • C 0 , 8
  • D 0 , 0
  • E 4 , 1 6

Q23:

Given that and , find the possible values of .

  • A
  • B12
  • C
  • D

Q24:

Given that u = 3 , 1 , and v = 2 , 5 , find the components of u v + .

  • A 1 , 6
  • B 6 , 5
  • C 1 , 6
  • D 5 , 4
  • E 2 , 3

Q25:

Given that u = 3 , 1 and v = 2 , 5 find the components of u + v .

  • A 8 , 3
  • B 6 , 5
  • C 1 , 4
  • D 5 , 6
  • E 1 , 4