Question
Find the vector equation of the plane passing through the intersection of the planes 
and the point (2, 1, 3).
Solution
The equations of given planes are
i.e.
i.e.
...(1)
and
i.e.
i.e.
...(2)
Any plane through the intersection of (1) and (2) is
(2x + y + 3z – 7) + k (2x + 5y + 3z – 9) = 0 ...(3)
∴ it passes through (2, 1, 3)
Putting
in (3), we get,
which is vector equation of required plane.
i.e.
i.e.
...(1)and
i.e.
i.e.
...(2)Any plane through the intersection of (1) and (2) is
(2x + y + 3z – 7) + k (2x + 5y + 3z – 9) = 0 ...(3)
∴ it passes through (2, 1, 3)
Putting
in (3), we get,which is vector equation of required plane.
