Worksheet: Polar Form of a Vector

In this worksheet, we will practice getting the polar form of a vector and proving that the two vectors are parallel or perpendicular.

Q1:

If 𝑂 𝐴 = 7 , 6 0 is the position vector, in polar form, of the point 𝐴 relative to the origin 𝑂 , find the 𝑥 𝑦 -coordinates of 𝐴 .

  • A 7 2 , 7 2
  • B 7 3 2 , 7 2
  • C 7 3 2 , 7 3 2
  • D 7 2 , 7 3 2

Q2:

If 𝑂 𝐶 = 4 3 , 3 𝜋 4 is the position vector, in polar form, of the point 𝐶 relative to the origin 𝑂 , find the 𝑥 𝑦 -coordinates of the point 𝐶 .

  • A 2 2 , 2 2
  • B 2 6 , 2 6
  • C 4 6 , 2 6
  • D 2 6 , 2 6
  • E 2 6 , 4 6

Q3:

Given the point 𝐴 4 3 , 4 , express, in polar form, its position vector relative to the origin point.

  • A 8 , 1 1 𝜋 3
  • B 8 2 , 1 1 𝜋 1 2
  • C 8 , 1 1 𝜋 1 2
  • D 8 , 1 1 𝜋 6

Q4:

Given that A = 6 , 1 5 , B = 𝑘 , 1 0 , and A B , find the value of 𝑘 .

Q5:

Trapezium 𝐴 𝐵 𝐶 𝐷 has vertices 𝐴 ( 1 0 , 1 1 ) , 𝐵 ( 𝑘 , 8 ) , 𝐶 ( 4 , 1 2 ) , and 𝐷 ( 2 , 6 ) . Given that 𝐴 𝐵 𝐶 𝐷 , find the value of 𝑘 .

Q6:

Let and

Find .

Which of the following is, therefore, true of the vectors?

  • AThey are perpendicular.
  • BIt does not tell anything about the vectors.
  • CThey are parallel but in opposite directions.
  • DThey are parallel but in the same direction.
  • EThe two vectors are equal in length.

Q7:

Given that the vectors and are perpendicular, find the value of .

Q8:

Given that the vectors and are perpendicular, find the value of 𝑥 .

Q9:

Given the point 𝐴 3 3 , 9 , express, in polar form, its position vector relative to the origin point.

  • A 6 3 , 1 0 𝜋 3
  • B 6 , 5 𝜋 6
  • C 1 2 , 5 𝜋 6
  • D 6 3 , 5 𝜋 3
  • E 1 2 , 1 0 𝜋 3

Q10:

Given the point 𝐴 2 3 , 6 , express, in polar form, its position vector relative to the origin point.

  • A 4 3 , 4 𝜋 3
  • B 4 , 𝜋 3
  • C 8 , 𝜋 3
  • D 4 3 , 2 𝜋 3
  • E 8 , 4 𝜋 3

Q11:

Given the point 𝐴 3 3 , 9 , express, in polar form, its position vector relative to the origin point.

  • A 6 3 , 8 𝜋 3
  • B 1 2 , 2 𝜋 3
  • C 6 , 2 𝜋 3
  • D 6 3 , 4 𝜋 3
  • E 6 , 8 𝜋 3

Q12:

Given the point 𝐴 2 3 , 2 , express, in polar form, its position vector relative to the origin point.

  • A 4 , 7 𝜋 3
  • B 4 , 7 𝜋 1 2
  • C 4 2 , 7 𝜋 1 2
  • D 4 , 7 𝜋 6
  • E 4 2 , 7 𝜋 3

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