Worksheet: Geometric Representation of Vectors

In this worksheet, we will practice representing a 2D vector graphically on the xy-plane given either its Cartesian coordinates or its polar coordinates.

Q1:

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
  • B
  • C
  • D
  • E

Q2:

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
  • C1
  • D13
  • E26

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

Q3:

What shape is formed by these vectors?

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

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