Worksheet: Vector Operations in 2D

Download

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−92,−152
  • B92,212
  • C−92,212
  • 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 AB−4.

  • A⟨−26,−28⟩
  • B⟨−26,20⟩
  • C⟨30,−28⟩
  • D⟨30,20⟩

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(−−2−2)ijk newtons
  • B−3i 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+.

  • A⟨−5,4⟩
  • B⟨0,1⟩
  • C⟨0,−20⟩
  • 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⟨−15,12⟩
  • 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⟨−6,30⟩

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?

  • A𝐷𝐶
  • B𝐵𝐴
  • C𝐸𝐹
  • D𝐹𝐷
  • E𝐶𝐷

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,−16⟩

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=34 and B=53. Find (+)⋅ABA.

Q15:

On a lattice, where 𝐴𝐶=⟨−5,−5⟩, 𝐵𝐶=⟨−12,6⟩, and 3+𝐴𝐵=⟨−8,13⟩C, 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,−4⟩C, 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
  • C5−6AB
  • D3−2AB

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,𝑚−13⟩ and |+|=7AB.

  • A−18, −6
  • B−5
  • 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
  • B−132,52
  • C52,52
  • D−132,112

Q25:

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

  • A3,−32
  • B−24,392
  • C3,392
  • D−24,−32

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.