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 equations.
Solution
Let 
be the position vectors of A, B, and C respectively.
Now, 
The vector equation of line through A 
and parallel to vector 
is
or 
Now taking 
the equation of line is
or 
Comparing the coefficients of x, y, z, we get,
which is cartesian equation of line.
