Find the equation of the plane through the line of intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0, and passing through the point (1, 1, 1).
Find the equation of the plane through the line of intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0, and passing through the point (1, 1, 1).

Answer:

Cartesian form of equation of plane through the line of intersection of planes:

 

 

 

 

 

 

 

14x + 14y + 14z – 84 + 6x + 9y + 12z + 15 = 0

20x + 23y + 26z – 69 = 0

The equation of the plane is 20x + 23y + 26z = 69.