Find the vector and Cartesian equations of the line through the point (5, 2, –4) and which is parallel to the vector 
vector equation of a line is

here  &
& 
so the vector equation of the line is

the Cartesian equation of the line is

where  are the coordinates of the fixed-point ‘a’, and
 are the coordinates of the fixed-point ‘a’, and  are coordinates of
 are coordinates of  .
.
so, the cartesian equation becomes as follows
