Lesson Worksheet: Polar Form of a Vector Mathematics

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In this worksheet, we will practice converting between rectangular and polar forms of a vector.

Q1:

Consider the vector ⟨−2,3⟩. Calculate the direction of the vector, giving your solution as an angle to the nearest degree measured counterclockwise from the positive 𝑥-axis.

Q2:

Fill in the blank: If Aij=−−, then the polar form of A is .

  • A√2,5𝜋4
  • B√2,7𝜋4
  • C√2,3𝜋4
  • D√2,𝜋4

Q3:

Fill in the blank: If 𝑃𝑀=4√3,4, then the polar form of vector 𝑃𝑀 is .

  • A8,𝜋6
  • B8,𝜋3
  • C8,𝜋4
  • D⟨8,𝜋⟩

Q4:

Consider the vector v with modulus 3 and an angle of 45∘ measured counter-clockwise from the positive 𝑥-axis. Using trigonometry, calculate the 𝑥- and 𝑦-components of the vector and, hence, write v in the form ⟨𝑥,𝑦⟩. Round your answer to two decimal places.

  • A⟨2.10,2.10⟩
  • B⟨2.12,2.12⟩
  • C⟨2.20,2.20⟩
  • D⟨2.11,2.11⟩
  • E⟨2.13,2.13⟩

Q5:

Fill in the blank: If ||=4Acm, then A=.

  • A√3,2
  • B2,2√3
  • C4√3,4
  • D2√3,2

Q6:

Fill in the blank: If A=7,5𝜋3, then A, in terms of the fundamental unit vectors, is .

  • A72−7√32ij
  • B7√32+72ij
  • C−7√32+72ij
  • D72+7√32ij

Q7:

Which of the following is the polar representation of A=2√3,2?

  • A
  • B
  • C
  • D
  • E

Q8:

Fill in the blank: If A=⟨6,𝜋⟩ and Bij=−3+4, then 𝐴𝐵=.

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

Q9:

If Aij=3+4, Bj=4, and C=6,𝜋10, then ||+||+||=ABC.

Q10:

Fill in the blank: If the force 𝐹=8N acts in the direction 30∘ east of north, where the east represents the positive 𝑥-axis and the north represents the positive 𝑦-axis, then 𝐹=.

  • A4−4√3ij
  • B4√3+4ij
  • C4+4√3ij
  • D4√3−4ij

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