Equation of plane

Question

Q) Find the equation of the plane through the three points

A (0,1,-1),  B (1,1,0),  C (1,2,0)

 

The answer is x -z = 1

Answer 1

The three points are A (0, 1, -1) , B(1, 1, 0), C(1, 2, 0)

Determine the direction vectors

Determine the normal vector

From the normal vector, the plane is - x + z + d = 0

Substitute any point to find d.

Second point (1, 1, 0)

- 1 + 0 + d = 0

d = 1

Substitute d = 1 in plane equation.

The plane is - x + z + 1 = 0

- x + z = - 1

Therefore, the plane equation is x - z = 1.