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Worksheet: Geometric Representation of Vectors

Q1:

Consider the vector 𝑣 with modulus 3 at an angle of 4 5 ∘ above the positive π‘₯ -axis. Using trigonometry, calculate the π‘₯ - and 𝑦 -components of the vector and, hence, write 𝑣 in the form  π‘₯ 𝑦  . Round your answer to three significant figures.

  • A  2 . 1 0 2 . 1 0 
  • B  2 . 2 0 2 . 2 0 
  • C  2 . 1 3 2 . 1 3 
  • D  2 . 1 2 2 . 1 2 
  • E  2 . 1 1 2 . 1 1 

Q2:

Consider the vector v =  3 βˆ’ 2  .

Which of the following graphs accurately represents the vector?

  • A
  • B
  • C
  • D
  • E

Calculate the modulus of the vector.

  • A √ 1 3
  • B √ 2 6
  • C1
  • D13
  • E26

Given that positive numbers represent measuring counter-clockwise, calculate the measure of the angle the vector makes with the positive π‘₯ -axis. Give your answer to 3 significant figures between βˆ’ 1 8 0 ∘ and 1 8 0 ∘ .

Q3:

What shape is formed by these vectors?

  • Aa rectangle
  • Ba rhombus
  • Ca kite
  • Da parallelogram
  • Ea square