Find an equation of the plane.?

Question

The plane that passes through the line of intersection of the planes x − z = 1 and y + 3z = 3 and is perpendicular to the plane x + y − 2z = 4

Answer 1

Step 1:

The plane equations are and

The plane passing through line of intersection of planes and is , where is a real number.

The plane equation is

The normal of the plane is .

Step 2:

The normal perpendicular to the normal of the plane .

So the dot product is zero.

.

Step 3:

Substitute the value of in equation (1).

The plane equation is .

Solution:

The plane equation is .