Lesson Worksheet: Vector Operations in 2D Mathematics • 12th Grade

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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=⟨6,11⟩, find 12A.

  • A⟨12,22⟩
  • B⟨12,11⟩
  • C⟨6,11⟩
  • D⟨3,11⟩
  • E⟨3,5.5⟩

Q2:

Given that A=⟨−1,−8⟩, find 3A.

  • A⟨−1,−24⟩
  • B⟨−24,−3⟩
  • C⟨−3,−24⟩
  • D⟨−3,−8⟩

Q3:

Given that A=⟨−1,2⟩ and B=⟨3,−6⟩, find 6+2AB.

  • A⟨0,24⟩
  • B⟨−12,0⟩
  • C⟨0,0⟩
  • D⟨12,0⟩
  • E⟨0,−24⟩

Q4:

Given that A=⟨2,−4⟩ and B=⟨−7,−6⟩, find AB−4.

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

Q5:

Given that A=⟨1,0,−1⟩ and C=⟨3,1,4⟩, determine 4−2(+4)OCA, where O is a zero vector.

  • A⟨−14,−2,0⟩
  • B⟨7,1,0⟩
  • C⟨−2,−2,−12⟩
  • D⟨2,−2,−16⟩

Q6:

If AB+=⟨1,2⟩ and AB−=⟨3,8⟩, find A.

  • A⟨2,5⟩
  • B⟨3,8⟩
  • C⟨1,2⟩
  • D⟨2,10⟩
  • E⟨4,10⟩

Q7:

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

  • A(8,−12)
  • B(−12,8)
  • C(14,−6)
  • D(−18,2)
  • E(16,−24)

Q8:

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

Q9:

Given that B=⟨−9,−3⟩, C=⟨−4,−2⟩, and D=⟨−2,9⟩, determine the vector A that satisfies the equation ABCD=−4+2−6.

  • A⟨56,−38⟩
  • B⟨−56,38⟩
  • C⟨−40,46⟩
  • D⟨40,−46⟩

Q10:

Given that A=⟨−3,5⟩, B=⟨2,0⟩, and C=⟨−4,5⟩, find |−2−2+2|ABC.

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