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Worksheet: Polar Form of a Vector

Q1:

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

  • A
  • B
  • C
  • D

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:

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

  • A
  • B9
  • C46
  • D11
  • E1

Q4:

Given the point 𝐴 ο€» βˆ’ 4 √ 3 , 4  , express, in polar form, its position vector relative to the origin point.

  • A ο€Ό 8 , 1 1 πœ‹ 3 
  • B ο€Ό 8 √ 2 , 1 1 πœ‹ 1 2 
  • C ο€Ό 8 , 1 1 πœ‹ 1 2 
  • D ο€Ό 8 , 1 1 πœ‹ 6 

Q5:

Given the point 𝐴 ( βˆ’ 5 , 5 ) , express, in polar form, its position vector relative to the origin point.

  • A ο€Ό 5 √ 2 , 3 πœ‹ 2 
  • B ο€Ό 1 0 √ 2 , 3 πœ‹ 8 
  • C ο€Ό 1 0 , 3 πœ‹ 8 
  • D ο€Ό 5 √ 2 , 3 πœ‹ 4 
  • E ο€Ό 1 0 , 3 πœ‹ 2 

Q6:

Given the point 𝐴 ( 1 0 , 1 0 ) , express, in polar form, its position vector relative to the origin point.

  • A ο€» 1 0 √ 2 , πœ‹ 2 
  • B ο€» 2 0 , πœ‹ 8 
  • C ο€» 2 0 √ 2 , πœ‹ 8 
  • D ο€» 1 0 √ 2 , πœ‹ 4 
  • E ο€» 2 0 √ 2 , πœ‹ 2 

Q7:

Given the point 𝐴 ο€» 3 √ 3 , βˆ’ 9  , express, in polar form, its position vector relative to the origin point.

  • A ο€Ό 6 √ 3 , 1 0 πœ‹ 3 
  • B ο€Ό 6 , 5 πœ‹ 6 
  • C ο€Ό 1 2 , 5 πœ‹ 6 
  • D ο€Ό 6 √ 3 , 5 πœ‹ 3 
  • E ο€Ό 1 2 , 1 0 πœ‹ 3 

Q8:

Given the point 𝐴 ο€» βˆ’ 4 √ 3 , βˆ’ 1 2  , express, in polar form, its position vector relative to the origin point.

  • A ο€Ό 8 √ 3 , 8 πœ‹ 3 
  • B ο€Ό 1 6 , 2 πœ‹ 3 
  • C ο€Ό 8 , 2 πœ‹ 3 
  • D ο€Ό 8 √ 3 , 4 πœ‹ 3 
  • E ο€Ό 8 , 8 πœ‹ 3 

Q9:

Given that the vectors and are perpendicular, find the value of π‘₯ .

Q10:

Let and

Find A B β‹… .

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.

Q11:

Given that , , and , find the value of .

Q12:

Given that the vectors and are perpendicular, find the value of π‘₯ .