A plane which passes through the point (3, 2, 0) and the line (x-4)/1 = (y-7)/5 = (z-4)/4 is

• 3D Geometry

A plane which passes through the point (3, 2, 0) and the line (x-4)/1 = (y-7)/5 = (z-4)/4 is

1. 2x - y + z = 5
2. x + 2y - z = 1
3. x - y + z = 1
4. x + y + z = 5

Answer

A line will be in a plane if

• 1. the normal to the plane is perpendicular to the line
• 2. a point on the line lies on the plane

In the given options, equation x - y + z = 1 is satisfied by (3, 2, 0) and (4, 7, 4).

The correct option is C.