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Length and Direction converted to (x, y)

52 degree vector

Say that you have been given a length and a direction and want to express them as a 2D column vector.

  1. Draw a sketch.
  2. Calculate x by projecting the length onto the x-axis
    (usually length*cos( θ ) )
  3. Calculate y by projecting the length onto the y-axis
    (usually length*sin( θ ) )
  4. Check answers against the sketch.

Of course, you can't wait to practice this (it brings back those fond memories of trigonometry.)


A vector has length 4 and orientation 150°. Represent the vector as a column matrix.