# 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 .

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**Q3: **

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

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**Q4: **

Given that , , and , find the value of .

**Q5: **

Trapezoid 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.

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**Q10: **

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

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**Q11: **

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

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**Q12: **

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

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**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.

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**Q16: **

Consider the vector .

Which of the following graphs accurately represents the vector?

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Calculate the modulus of the vector.

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

**Q17: **

If the force acts in the direction east of north, then .

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**Q18: **

If , then vector , in terms of the fundamental unit vectors, equals .

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**Q19: **

If , then the polar form of is .

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**Q20: **

If , then the polar form of vector is .

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**Q21: **

If and rotates around the origin with an angle of measure anticlockwise, then the polar form of vector after rotation is .

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**Q22: **

If , then .

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**Q23: **

If the polar form of is , then the polar form of is .

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**Q24: **

If , , and , then .

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**Q25: **

If and , then .

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