Question
Find the vector equation of the plane passing through the point A(2, 2, –1), B(3, 4, 2) and C (7, 0, 6). Also find the cartesian equation of the plane.
Solution
Here, 
The vector equations of plane is
or 
The Cartesian equation of plane is
or 
or (or – 2) (14 + 6) – (y – 2) (7 – 15) + (z + 1) (–2 – 10) = 0
or 20 (x – 2) + 8 (y – 2) – 12 (z + 1) = 0
or 5 (x – 2) + 2 (y – 2) – 3 (z + 1) = 0
or 5 x – 10 + 2y – 4 – 3 z – 3 = 0
or 5 x + 2 y – 3 z – 17 = 0
