Lesson Worksheet: Adding and Subtracting Vectors in 2D Mathematics

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

Q1:

Given that A=⟨1,9⟩ and B=⟨−4,1⟩, find AB−.

  • A⟨−8,−5⟩
  • B⟨10,−3⟩
  • C⟨5,8⟩
  • D⟨8,5⟩
  • E⟨−3,10⟩

Q2:

Given that A=⟨9,5⟩, B=⟨−10,3⟩, and C=⟨−3,6⟩, find ABC+−.

  • A⟨−22,4⟩
  • B⟨2,2⟩
  • C⟨22,−4⟩
  • D⟨16,8⟩
  • E⟨−4,14⟩

Q3:

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⟩

Q4:

Given that A=⟨9,−12⟩ and B=⟨13,−1⟩, find AB+.

  • A⟨−22,13⟩
  • B⟨13,−22⟩
  • C⟨22,−13⟩
  • D⟨−13,22⟩

Q5:

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

Q6:

Are there any vector u and v for which ‖+‖>‖‖+‖‖uvuv?

  • ANo
  • BYes

Q7:

Let u=⟨3,−2⟩ and v=⟨−9,5⟩.

What are the components of uv+?

  • A⟨3,−6⟩
  • B⟨8,−11⟩
  • C⟨12,−7⟩
  • D⟨−6,3⟩
  • E⟨−27,−10⟩

What are the components of vu+?

  • A⟨12,−7⟩
  • B⟨8,−11⟩
  • C⟨3,−6⟩
  • D⟨−6,3⟩
  • E⟨−27,−10⟩

Q8:

Consider the vectors u=⟨1,2⟩ and v=⟨−3,−1⟩.

What is the magnitude of u? Give your answer correct to two decimal places if needed.

What is the magnitude of v? Give your answer correct to two decimal places if needed.

What is the magnitude of uv+? Give your answer correct to two decimal if needed.

Q9:

Consider the vectors u=⟨5,−2⟩ and v=⟨−5,2⟩.

What is the magnitude of u? Give your answer correct to two decimal places if needed.

What is the magnitude of v? Give your answer correct to two decimal places if needed.

What is the magnitude of uv+? Give your answer correct to two decimal places if needed.

Q10:

Given that Aij=−5+10 and Bij=−4−5, where i and j are two perpendicular unit vectors, find AB−.

  • A−15+ij
  • B15−ij
  • C−9+5ij
  • D−+15ij
  • E5−9ij

Q11:

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⟩

Q12:

If A=⟨6,−4,7⟩, and B=⟨5,6,4⟩, determine AB+.

  • A⟨1,−10,3⟩
  • B⟨11,2,11⟩
  • C⟨−1,0,−3⟩
  • D⟨2,11,11⟩

Q13:

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

  • Az
  • Bu

Q14:

Is it always true that 𝐴𝐵+𝐶𝐷=𝐴𝐷?

  • AYes
  • BNo

Q15:

Is it always true that 𝐴𝐵+𝐵𝐶=𝐴𝐶?

  • ANo
  • BYes

Q16:

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

  • Az
  • Bu

Q17:

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

What are the components of u?

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

What are the components of v?

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

What are the components of uv+?

  • A⟨2,1⟩
  • B⟨−2,−1⟩
  • C⟨4,−5⟩
  • D⟨4,5⟩
  • E⟨−4,−5⟩

Q18:

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

Q19:

Find the sum of the vectors 𝐴𝐵=3−4ij and 𝐶𝐷=−5−5ij.

  • A−10−1ij
  • B−2−1ij
  • C−2−9ij
  • D8−1ij
  • E−1−10ij

Q20:

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⟩

Q21:

𝐴𝐵𝐶𝐷𝐸𝐹 is a regular hexagon. 𝐴𝐹 is parallel to 𝑎𝐵, and 𝐸𝐹 is parallel to 𝑎𝐷. Express 𝐴𝐸 in terms of u and v.

  • A2+uv
  • B−2+uv
  • C−2+vu
  • D−+uv
  • E2+vu

Q22:

Does the vector sum ⟨1,2⟩+⟨2,3,1⟩ have a solution?

  • ANo
  • BYes

Q23:

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

What are the components of u?

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

What are the components of v?

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

What are the components of uv+?

  • A⟨−5,−1⟩
  • B⟨5,−1⟩
  • C⟨5,1⟩
  • D⟨1,−5⟩
  • E⟨−1,5⟩

Q24:

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

What are the components of u?

  • A⟨2,3⟩
  • B⟨3,3⟩
  • C⟨1,4⟩
  • D⟨−1,3⟩
  • E⟨1,3⟩

What are the components of v?

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

What are the components of uv+?

  • A⟨4,6⟩
  • B⟨−4,5⟩
  • C⟨5,5⟩
  • D⟨4,4⟩
  • E⟨4,5⟩

Q25:

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

What are the components of u?

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

What are the components of v?

  • A⟨0,−4⟩
  • B⟨0,4⟩
  • C⟨−4,−4⟩
  • D⟨3,−4⟩
  • E⟨4,−4⟩

What are the components of uv+?

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

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