Section Content

At the end of this section, students should be able to:

  • express a vector in the form \(\begin{pmatrix} x\\y \\z \end{pmatrix}\) or \(xi+yj+zk\) where \(i, j\) and \(k\) are unit vectors in the direction of \(x-, y-\) and \(z-\) axis respectively;
  • define equality of two vectors;
  • add and subtract vectors;
  • multiply a vector by a scalar quantity;
  • derive and use unit vectors, position vectors and displacement vectors;
  • find the magnitude and direction of a vector;
  • find the angle between two vectors using scalar product;
  • find the equation of a line in vector form, parametric form, Cartesian form, given a point on the line and a vector parallel to the line;
  • determine whether two lines are parallel, intersecting or skewed;
  • find the equation of the plane, in the form \(xi+yj+zk=d\), \(r.n=d\), given a point in the plane and the normal to the plane.