Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Polar Form of a Vector

Sample Question Videos

Worksheet • 12 Questions • 1 Video

Q1:

If οƒ  𝑂 𝐴 = ( 7 , 6 0 ) ∘ is the position vector, in polar form, of the point 𝐴 relative to the origin 𝑂 , find the π‘₯ 𝑦 -coordinates of 𝐴 .

  • A ο€Ώ 7 2 , 7 √ 3 2 
  • B ο€Ώ 7 √ 3 2 , 7 2 
  • C ο€Ώ 7 √ 3 2 , 7 √ 3 2 
  • D ο€Ό 7 2 , 7 2 

Q2:

If οƒ  𝑂 𝐢 = ο€Ό 4 √ 3 , 3 πœ‹ 4  is the position vector, in polar form, of the point 𝐢 relative to the origin 𝑂 , find the π‘₯ 𝑦 -coordinates of the point 𝐢 .

  • A ο€» βˆ’ 2 √ 6 , 2 √ 6 
  • B ο€» βˆ’ 2 √ 6 , 4 √ 6 
  • C ο€» 2 √ 6 , βˆ’ 2 √ 6 
  • D ο€» βˆ’ 4 √ 6 , 2 √ 6 
  • E ο€Ώ βˆ’ √ 2 2 , √ 2 2 

Q3:

Trapezium 𝐴 𝐡 𝐢 𝐷 has vertices 𝐴 ( 1 0 , 1 1 ) , 𝐡 ( π‘˜ , 8 ) , 𝐢 ( 4 , βˆ’ 1 2 ) , and 𝐷 ( βˆ’ 2 , 6 ) . Given that οƒ  𝐴 𝐡 β«½ οƒ  𝐢 𝐷 , find the value of π‘˜ .

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‹ 6 
  • 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‹ 3 

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‹ 4 
  • B ο€Ό 1 0 , 3 πœ‹ 2 
  • C ο€Ό 1 0 √ 2 , 3 πœ‹ 8 
  • D ο€Ό 1 0 , 3 πœ‹ 8 
  • E ο€Ό 5 √ 2 , 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‹ 4 
  • B ο€» 2 0 √ 2 , πœ‹ 2 
  • C ο€» 2 0 , πœ‹ 8 
  • D ο€» 2 0 √ 2 , πœ‹ 8 
  • E ο€» 1 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 , 5 πœ‹ 3 
  • B ο€Ό 1 2 , 1 0 πœ‹ 3 
  • C ο€Ό 6 , 5 πœ‹ 6 
  • D ο€Ό 1 2 , 5 πœ‹ 6 
  • E ο€Ό 6 √ 3 , 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 , 4 πœ‹ 3 
  • B ο€Ό 8 , 8 πœ‹ 3 
  • C ο€Ό 1 6 , 2 πœ‹ 3 
  • D ο€Ό 8 , 2 πœ‹ 3 
  • E ο€Ό 8 √ 3 , 8 πœ‹ 3 

Q9:

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

Q10:

Let and

Find .

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

  • AThey are perpendicular.
  • BThe two vectors are equal in length.
  • CThey are parallel but in the same direction.
  • DIt does not tell anything about the vectors.
  • EThey are parallel but in opposite directions.

Q11:

Given that ⃑ 𝐴 = ( βˆ’ 6 , βˆ’ 1 5 ) , ⃑ 𝐡 = ( π‘˜ , βˆ’ 1 0 ) , and ⃑ 𝐴 β«½ ⃑ 𝐡 , find the value of π‘˜ .

Q12:

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

Preview