Question
Find the vector and Cartesian equations of the line through the point (5, 2, – 4) and which is parallel to the vector 
Solution
Since the line passes through the point (5, 2, 4) and is parallel to the vector 
Let
be the position vector of any point on the line.
∴ the vector equation of line is
or
Taking
the equation of line is
Comparing the coefficients of
we get,
or
which is cartesian equation of line.
Let
be the position vector of any point on the line.∴ the vector equation of line is
or
Taking
the equation of line isComparing the coefficients of
we get,or
which is cartesian equation of line.
