Worksheet: Vector Operations in 2D

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

Q1:

Given that A=0,1 and B=3,6, find 32()AB.

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

Q2:

Given that A=0,1 and |𝑘|=12A, find the possible values of 𝑘.

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

Q3:

Given that A=2,4 and B=7,6, find AB4.

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

Q4:

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

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

Q5:

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

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

Q6:

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

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

Q7:

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

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

Q8:

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

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

Q9:

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

What are the components of u?

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

What are the components of v?

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

What are the components of uv+?

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

Q10:

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

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

Q11:

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

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

Q12:

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

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

Q13:

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

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

Q14:

A = 3 4 and B=53. Find (+)ABA.

Q15:

On a lattice, where 𝐴𝐶=5,5, 𝐵𝐶=12,6, and 3+𝐴𝐵=8,13C, determine the coordinates of the point 𝐵.

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

Q16:

On a lattice, where 𝐴𝐶=3,3, 𝐵𝐶=13,7, and 2+2𝐴𝐵=4,4C, find the coordinates of the point 𝐶.

  • A ( 8 , 1 2 )
  • B ( 1 2 , 8 )
  • C ( 1 4 , 6 )
  • D ( 1 8 , 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 + 1 0 A B
  • B + 6 A B
  • C 5 6 A B
  • D 3 2 A 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 A B = +
  • B C A B = 3 +
  • C C A B = + 3
  • D C A B = 2

Q19:

When is it true that uvvu+=+?

  • Afor any vectors u and v
  • Bonly when u and v are not perpendicular
  • Conly when u and v are equivalent
  • Donly when u and v are perpendicular
  • Eonly when u and v are parallel

Q20:

When is it true that +=+uvuv?

  • Aalways
  • Bwhen u and v are perpendicular vectors
  • Cnever
  • Dwhen u and v are equivalent vectors
  • Ewhen u and v are parallel vectors

Q21:

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

  • A | + | V W
  • B | | + | | V W
  • CThey are both the same.

Q22:

Find all the possible values of 𝑚 given A=4,3,1, B=6,6,𝑚13 and |+|=7AB.

  • A 1 8 , 6
  • B 5
  • C18, 6
  • D1

Q23:

Given that A=8,3 and B=5,3, find 12()AB.

  • A 3 2 , 3
  • B 1 3 2 , 0
  • C 3 2 , 0
  • D 1 3 2 , 3

Q24:

Given that A=4,8 and B=9,3, find 12(+)AB.

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

Q25:

Given that A=7,6 and B=9,7, find 32()AB.

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

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