Lesson Worksheet: Properties of Operations on Vectors Mathematics

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In this worksheet, we will practice using the properties of addition and multiplication on vectors.

Q1:

What is the addition property that shows that aa0+(−)=?

  • ACommutative property
  • BAssociative property
  • CAddition identity property
  • DDistributive property
  • EAdditive inverse property

Q2:

Which of the following properties of vector operations is incorrect?

  • Aa0a+=
  • Baa0+(−)=
  • Cabba+=+
  • Dabcabc+(+)=(+)+
  • E(𝑐+𝑑)=𝑐𝑑aa

Q3:

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⟩

Q4:

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

  • ANo
  • BYes

Q5:

Complete the following: ⟨1,9⟩+⟨5,2⟩=⟨5,2⟩+⟨,⟩.

  • A1,9
  • B0,0
  • C−1,−9
  • D1,5
  • E5,2

Q6:

Given that a=⟨1,5⟩ and b=⟨6,2⟩, find aba++(−).

  • A⟨7,7⟩
  • B⟨0,0⟩
  • C⟨−6,−2⟩
  • D⟨1,5⟩
  • E⟨6,2⟩

Q7:

Complete the following: 2(⟨2,5⟩+⟨5,1⟩)=⟨,⟩+⟨10,2⟩.

  • A4,10
  • B4,2
  • C10,2
  • D2,5
  • E4,5

Q8:

Given that a=⟨9,1⟩, find a0+.

  • A⟨−1,−9⟩
  • B⟨1,9⟩
  • C⟨0,0⟩
  • D⟨9,1⟩
  • E⟨−9,−1⟩

Q9:

What is the property that shows that 𝑐(+)=𝑐+𝑐abab?

  • ADistributive property
  • BCommutative property
  • CAdditive inverse property
  • DAddition identity property
  • EAssociative property

Q10:

Consider that ⃑𝑎=(1,6), ⃑𝑏=(3,7), and ⃑𝑐=(6,3).

Find ⃑𝑎+⃑𝑏+⃑𝑐.

  • A(9,16)
  • B(9,17)
  • C(16,10)
  • D(10,16)
  • E(10,17)

Find ⃑𝑎+⃑𝑏+⃑𝑐.

  • A(9,17)
  • B(10,16)
  • C(16,10)
  • D(9,16)
  • E(10,17)

Does ⃑𝑎+⃑𝑏+⃑𝑐 equal ⃑𝑎+⃑𝑏+⃑𝑐?

  • AYes
  • BNo

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