Question
Find the equation of the plane passing through the points (0. – 1, 0), (1, 1, 1) and (3, 3,0).
Solution
The equation of any plane through the points (0, – 1, 0) is
a (x – 0) + b (y + 1) + c (z – 0) = 0 ...(1)
∴ it passes through (1, 1, 1)
∴ a + 2 b + c = 0 ...(2)
Again plane passes through (3, 3, 0)
∴ 3 a + 4 b + 0 c = 0 ...(3)
Solve (2) and (3), we get,
Putting values of a, b,c in (1), we get,
4 k x – 3 k (y + 1) + 2 k z = 0
or 4 x – 3 y + 2 z = 3
which is required equation of plane.
