Question
Find the equation of the plane passing through the points (0, –1, –1), (4, 5, 1) and (3, 9, 4).
Solution
The equation of plane passing through (0, – 1,–1) is
A (x – 0) + B(y + 1) + C(z + 1) = 0 ...(1)
∴ it passes through (4, 5, 1)
∴ A(4 – 0) + B(5 + 1) + C( 1 + 1) = 0
∴ 4A + 6B + 2C = 0 ⇒ 2A + 3B + C = 0 ...(2)
Again plane (1) passes through (3, 9, 4)
∴ A(3 – 0) + B(9 + 1) + C(4 + 1) = 0
∴ 3A + 10B + 5C = 0 ....(3)
Solving (2) and (3), we get,
Putting values of A, B, C in (1), we get,
5 k (x – 0) – 7 k (y + 1) + 11 k (z + 1) = 0
or 5 x – 7 y – 7 + 11 z + 11 = 0
or 5 x – 7 y + 11 z + 4 = 0
which is required equation of plane.
