Lesson Worksheet: Polar Form of a Vector Mathematics

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


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.


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

  • A2,5𝜋4
  • B2,7𝜋4
  • C2,3𝜋4
  • D2,𝜋4


Fill in the blank: If 𝑃𝑀=43,4, then the polar form of vector 𝑃𝑀 is .

  • A8,𝜋6
  • B8,𝜋3
  • C8,𝜋4
  • D8,𝜋


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.

  • A2.10,2.10
  • B2.12,2.12
  • C2.20,2.20
  • D2.11,2.11
  • E2.13,2.13


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

  • A3,2
  • B2,23
  • C43,4
  • D23,2


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

  • A72732ij
  • B732+72ij
  • C732+72ij
  • D72+732ij


Which of the following is the polar representation of A=23,2?

  • A
  • B
  • C
  • D
  • E


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

  • A3,4
  • B3,4
  • C3,4
  • D3,4


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


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=.

  • A443ij
  • B43+4ij
  • C4+43ij
  • D434ij

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