Lesson Worksheet: Adding and Subtracting Vectors in 2D Mathematics • 12th Grade

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In this worksheet, we will practice adding and subtracting vectors in 2D.

Q1:

If a=⟨3,2⟩ and b=⟨4,−1⟩, find ab+.

  • A⟨7,3⟩
  • B⟨7,1⟩
  • C⟨5,−5⟩
  • D⟨2,6⟩
  • E⟨5,3⟩

Q2:

Let z be the zero vector. What is zu+ equal to for any vector u?

  • Az
  • Bu

Q3:

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⟩

Q4:

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

What are the components of u?

  • A⟨2,2⟩
  • B⟨2,1⟩
  • C⟨−2,2⟩
  • D⟨2,4⟩
  • E⟨−2,1⟩

What are the components of v?

  • A⟨3,−4⟩
  • B⟨3,4⟩
  • C⟨−3,−4⟩
  • D⟨2,−4⟩
  • E⟨−3,4⟩

What are the components of uv+?

  • A⟨−1,3⟩
  • B⟨1,3⟩
  • C⟨−1,−3⟩
  • D⟨1,−3⟩
  • E⟨1,4⟩

Q5:

If ‖‖=5u and ‖‖=2v, what is the smallest that ‖+‖uv could be?

Q6:

Given the vectors 𝐴𝐵=3−4ij and 𝐶𝐷=−5−5ij, calculate 𝐴𝐵−𝐶𝐷.

  • A8+9ij
  • B−2−9ij
  • C−8−ij
  • D2+9ij
  • E8+ij

Q7:

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

  • A⟨4,−2⟩
  • B⟨10,2⟩
  • C⟨0,2⟩
  • D⟨0,−2⟩

Q8:

Given that A=⟨−4,5⟩ and AB+=⟨2,7⟩, find B.

  • A⟨−6,2⟩
  • B⟨−2,12⟩
  • C⟨6,−2⟩
  • D⟨−6,−2⟩
  • E⟨6,2⟩

Q9:

Given that A=⟨7,−1⟩ and AB−=⟨3,−2⟩, find AB+.

  • A⟨−11,−1⟩
  • B⟨−11,0⟩
  • C⟨11,−1⟩
  • D⟨11,0⟩
  • E⟨4,1⟩

Q10:

Given that A=⟨3,−2⟩, B=⟨−5,4⟩, and ABC−+=⟨6,−1⟩, find C.

  • A⟨8,−3⟩
  • B⟨14,−7⟩
  • C⟨−14,7⟩
  • D⟨−2,5⟩
  • E⟨2,−5⟩

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