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.

  • A92,152
  • B92,212
  • C92,212
  • D92,152

Q2:

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

  • A12,12
  • B12
  • C112,112
  • D112

Q3:

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

  • A26,28
  • B26,20
  • C30,28
  • D30,20

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(22)ijk newtons
  • B3i newtons
  • C(+2+2)ijk newtons
  • D(3++)ijk newtons
  • E3i newtons

Q5:

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

  • A5,4
  • B0,1
  • C0,20
  • D0,9
  • E0,1

Q6:

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

  • A3,1
  • B0,0
  • C15,12
  • D0,2
  • E4,6

Q7:

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

  • A5,1
  • B0,0
  • C4,6
  • D6,4
  • E6,30

Q8:

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

  • A4,2
  • B2,4
  • C2,4
  • D0,0
  • E4,2

Q9:

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

What are the components of u?

  • A4,1
  • B5,1
  • C4,2
  • D4,1
  • E5,2

What are the components of v?

  • A5,1
  • B6,1
  • C6,1
  • D5,1
  • E5,2

What are the components of uv+?

  • A1,2
  • B2,3
  • C1,2
  • D1,3
  • E1,3

Q10:

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

  • A𝐷𝐶
  • B𝐵𝐴
  • C𝐸𝐹
  • D𝐹𝐷
  • E𝐶𝐷

Q11:

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

  • A0,0
  • B4,8
  • C0,8
  • D4,8
  • E4,16

Q12:

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

  • A1,6
  • B1,6
  • C6,5
  • D2,3
  • E5,4

Q13:

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

  • A1,4
  • B8,3
  • C1,4
  • D6,5
  • E5,6

Q14:

A=34 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(10,3)
  • C(17,14)
  • 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(8,12)
  • B(12,8)
  • C(14,6)
  • D(18,2)
  • E(16,24)

Q17:

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

  • A7+10AB
  • B+6AB
  • C56AB
  • D32AB

Q18:

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

  • ACAB=+
  • BCAB=3+
  • CCAB=+3
  • DCAB=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|+|VW
  • B||+||VW
  • CThey are both the same.

Q22:

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

  • A18, 6
  • B5
  • C18, 6
  • D1

Q23:

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

  • A32,3
  • B132,0
  • C32,0
  • D132,3

Q24:

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

  • A52,112
  • B132,52
  • C52,52
  • D132,112

Q25:

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

  • A3,32
  • B24,392
  • C3,392
  • D24,32

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