# Worksheet: Polar Form of a Vector

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

**Q2: **

If is the position vector, in polar form, of the point relative to the origin , find the -coordinates of the point .

- A
- B
- C
- D
- E

**Q3: **

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

- A
- B
- C
- D

**Q4: **

Given that , , and , find the value of .

**Q5: **

Trapezium has vertices , , , and . Given that , find the value of .

**Q6: **

Let and

Find .

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

- AThey are parallel and in the same direction.
- BIt does not tell anything about the vectors.
- CThey are perpendicular.
- DThe two vectors are equal in length.
- EThey are parallel but in opposite directions.

**Q7: **

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

**Q8: **

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

**Q9: **

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

- A
- B
- C
- D
- E

**Q10: **

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

- A
- B
- C
- D
- E

**Q11: **

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

- A
- B
- C
- D
- E

**Q12: **

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

- A
- B
- C
- D
- E

**Q14: **

Consider the vector . Calculate the direction of the vector, giving your solution as an angle to the nearest degree measured counterclockwise from the positive -axis.

**Q15: **

Consider the vector with modulus 3 at an angle of above the positive -axis. Using trigonometry, calculate the - and -components of the vector and, hence, write in the form Round your answer to three significant figures.

- A
- B
- C
- D
- E

**Q16: **

Consider the vector .

Which of the following graphs accurately represents the vector?

- A
- B
- C
- D
- E

Calculate the modulus of the vector.

- A
- B
- C26
- D1
- E13

Given that positive numbers represent measuring counter-clockwise, calculate the measure of the angle the vector makes with the positive -axis. Give your answer to 3 significant figures between and .