# Worksheet: Polar Form of a Vector

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

Q1:

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

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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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• E

Q12:

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

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Q13:

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.

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
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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 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 . • A
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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 .

• A6
• B11
• C10
• D15

Q25:

If and , then .

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