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