Find an equation of the plane The plane that passes through the line of intersection of the planes x - z = 1 and y + 3z = 2 and is perpendicular to the plane x + y - 4z = 3.

2x - y + 5z + 3 = 0

Step-by-step explanation:

The two vectors can be shown like this:

Any plane passing through the intersection x - z = 1 and y + 3z = 2 can be given by:

(x - z - 1) + k (y + 3z - 2) = 0

This is the same as

x - 1 + z (-1 + 3k) + y (k) - 2k = 0

This is perpendicular to x + y - 4 z = 0

Using the dot product of normal vectors you can find the value of k.

The value of k will be 4/11

Using the value of k gives 2x - y + 5z + 3 = 0