Question
Find the vector equation of a line passing through a point with position vector 
and parallel to the line joining the points with position vectors 
and 
Also, find the cartesian equivalent of this equation.
Solution
Let 
be the position vector of A and 
be position vectors of B and C.
The vector equation of line through 
and parallel to vector 
is
or 
Now taking 
, the equation of line is
or 
Comparing the coefficients of 
we get, x = λ + 1, y = 2 λ – 2, z = – (2 λ + 3)
or 
which is cartesian equation of line.
