Question
Find the vector equation of the line passing through the point (3, 1, 2) and perpendicular to the plane 
Find also the point of intersection of this line and plane.
Solution
The equation of plane is 
....(1)
Vector along the normal to the plane is
Now required line passes through point (3, 1, 2) with position vector
and is parallel to the vector 
...(2)
∴ equation of line is
Now line (2) meets plane (1) when
Putting this value of λ in (2), we get the position vector of the point of intersection of (1) and (2) as
....(1)Vector along the normal to the plane is
Now required line passes through point (3, 1, 2) with position vector
and is parallel to the vector ...(2)∴ equation of line is
Now line (2) meets plane (1) when
Putting this value of λ in (2), we get the position vector of the point of intersection of (1) and (2) as
