Cartesian components of vectors

This resource from Mathcentre explores vectors in two and three-dimensions, how to calculate the length of a position vector and the angle between a position vector and an x axis. After reading through the text and completed the exercise questions, students should be able to: 

  • coordinate unit vectors in two dimensions and in three dimensions
  • determine whether a set of coordinate axes in three dimensions is labelled as a right-handed system
  • express the position vector of a point in terms of the coordinate unit vectors, and as a column vector
  • calculate the length of a position vector, and the angle between a position vector and a coordinate axis
  • write down a unit vector in the same direction as a given position vector
  • express a vector between two points in terms of the coordinate unit vectors

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