Question
Show that the line whose vector equation is 
lies in the plane 
whose vector equation is 
Solution
The equation of plane is
...(1)
The equation of line is
...(2)
Now the line (2) will lie in plane (1)
(i) if the point with position vector
lies in the plane
i.e. if
i.e. if (1) (1) + (1) (2) + (0) (– 1) = 3
i.e. if 1 + 2 + 0 = 3
i.e. if 3 = 3, which is true.
and (ii)
is perpendicular to 
i.e., if
i.e. if (1) (2) + (2) (1) + (– 1) (4) = 0
i.e. if 2 + 2 – 4 = 0, which is true
∴ line (2) lies in plane (1).
...(1)The equation of line is
...(2)Now the line (2) will lie in plane (1)
(i) if the point with position vector
lies in the planei.e. if
i.e. if (1) (1) + (1) (2) + (0) (– 1) = 3
i.e. if 1 + 2 + 0 = 3
i.e. if 3 = 3, which is true.
and (ii)
is perpendicular to i.e., if
i.e. if (1) (2) + (2) (1) + (– 1) (4) = 0
i.e. if 2 + 2 – 4 = 0, which is true
∴ line (2) lies in plane (1).
