Question

Find the equation of the plane passing through the points (−2, 6, 6), (1, −1, 0) and (1, 2, −1).

Answer 1

Given:

(−2, 6, 6), (1, −1, 0) and (1, 2, −1)

x₁, y₁, z₁

x₂, y₂, z₂

x₃, y₃, z₃

We know that, Cartesian eqn. given by

`|(x - x_1, y - y_1, z - z_1),(x_2 - x_1, y_2 - y_1, z_2 - z_1),(x_3 - x_2, y_3 - y_2, z_3 - z_2)| = 0`

On putting values

`|(x + 2, y − 6, z − 6),(1 + 2, - 1 - 6, 0 - 6),(1 - 1, 2 + 1, -1 - 0)| = 0`

`|(x + 2, y - 6, z - 6),(3, -7, -6),(0, 3, -1)| = 0`

(x + 2)(7 + 18) − (y − 6)(− 3) + (z − 6)(9) = 0

7x + 18x + 14 + 36 + 3y − 18 + 9z − 54 = 0

25x + 3y + 9z − 22 = 0