Worksheet: Vector Operations

In this worksheet, we will practice solving operations on vectors algebraically such as vector addition, vector subtraction, and scalar multiplication.

Q1:

Given that 𝐴 = ( 0 , 1 ) and 𝐵 = ( 3 , 6 ) , find 3 2 𝐴 𝐵 .

  • A 9 2 , 1 5 2
  • B 9 2 , 1 5 2
  • C 9 2 , 2 1 2
  • D 9 2 , 2 1 2

Q2:

Given that 𝐴 = ( 0 , 1 ) and 𝑘 𝐴 = 1 2 , find the possible values of 𝑘 .

  • A 1 1 2 , 1 1 2
  • B12
  • C 1 1 2
  • D 1 2 , 1 2

Q3:

Given that 𝐴 = ( 2 , 4 ) and 𝐵 = ( 7 , 6 ) , find 𝐴 4 𝐵 .

  • A ( 2 6 , 2 0 )
  • B ( 2 6 , 2 8 )
  • C ( 3 0 , 2 8 )
  • D ( 3 0 , 2 0 )

Q4:

A force of newtons is being applied to an object. What other force should be applied to achieve a total force of newtons?

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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

Q11:

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

Q12:

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

Q13:

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

Q14:

and Find .

Q15:

On a lattice, where 𝐴 𝐶 = ( 5 , 5 ) , 𝐵 𝐶 = ( 1 2 , 6 ) , and 3 𝐶 + 𝐴 𝐵 = ( 8 , 1 3 ) , determine the coordinates of the point 𝐵 .

  • A ( 1 7 , 1 4 )
  • B ( 1 0 , 3 )
  • C ( 1 , 6 )
  • D ( 7 , 2 )

Q16:

On a lattice, where 𝐴 𝐶 = ( 3 , 3 ) , 𝐵 𝐶 = ( 1 3 , 7 ) , and 2 𝐶 + 2 𝐴 𝐵 = ( 4 , 4 ) , find the coordinates of the point 𝐶 .

  • A ( 1 8 , 2 )
  • B ( 1 2 , 8 )
  • C ( 1 4 , 6 )
  • D ( 8 , 1 2 )
  • E ( 1 6 , 2 4 )

Q17:

Given that 𝐴 = ( 4 , 1 ) and 𝐵 = ( 2 , 1 ) , express 𝐶 = ( 8 , 1 ) in terms of 𝐴 and 𝐵 .

  • A 7 𝐴 + 1 0 𝐵
  • B 𝐴 + 6 𝐵
  • C 5 𝐴 6 𝐵
  • D 3 𝐴 2 𝐵

Q18:

If 𝐴 = ( 1 , 2 , 1 ) , 𝐵 = ( 1 , 1 , 0 ) , and 𝐶 = ( 2 , 1 , 1 ) , express 𝐶 in terms of 𝐴 and 𝐵 .

  • A 𝐶 = 2 𝐴 𝐵
  • B 𝐶 = 3 𝐴 + 𝐵
  • C 𝐶 = 𝐴 + 𝐵
  • D 𝐶 = 𝐴 + 3 𝐵

Q19:

When is it true that u v v u + = + ?

  • Aonly when u and v are parallel
  • Bonly when u and v are equivalent
  • Conly when u and v are perpendicular
  • Dfor any vectors u and v
  • Eonly when u and v are not perpendicular

Q20:

When is it true that + = + u v u v ?

  • Anever
  • Balways
  • Cwhen u and v are equivalent vectors
  • Dwhen u and v are parallel vectors
  • Ewhen u and v are perpendicular vectors

Q21:

𝑉 and 𝑊 are two vectors, where 𝑉 = ( 1 , 5 , 2 ) and 𝑊 = ( 3 , 1 , 1 ) . Comparing 𝑉 + 𝑊 and 𝑉 + 𝑊 , which quantity is larger?

  • AThey are both the same.
  • B 𝑉 + 𝑊
  • C 𝑉 + 𝑊

Q22:

Find all the possible values of 𝑚 given 𝐴 = ( 4 , 3 , 1 ) , 𝐵 = ( 6 , 6 , 𝑚 1 3 ) and 𝐴 + 𝐵 = 7 .

  • A 5
  • B1
  • C 1 8 , 6
  • D18, 6

Q23:

Given that 𝐴 = ( 3 , 3 ) and 𝐵 = ( 4 , 6 ) , find 1 2 𝐴 + 𝐵 .

  • A 7 2 , 3 2
  • B 1 2 , 3 2
  • C 1 2 , 9 2
  • D 7 2 , 9 2

Q24:

Given that 𝐴 = ( 9 , 4 ) and 𝐵 = ( 3 , 2 ) , find 1 2 𝐴 + 𝐵 .

  • A ( 3 , 3 )
  • B ( 6 , 3 )
  • C ( 6 , 1 )
  • D ( 3 , 1 )

Q25:

Given that 𝐴 = ( 7 , 6 ) and 𝐵 = ( 9 , 7 ) , find 3 2 𝐴 𝐵 .

  • A 2 4 , 3 2
  • B 3 , 3 2
  • C 3 , 3 9 2
  • D 2 4 , 3 9 2

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