Find the vector equation of the plane passing through the points (3, 4, 2) and (7, 0, 6) and perpendicular to the plane 2x – 5y – 15 = 0. Also, show that the plane thus obtained contains the line

Let the equation of the plane be …… (1)

Plane is passing through (3, 4, 2) and (7, 0, 6)

Required plane is perpendicular to 2x – 5y – 15 = 0

2b = 5a

Solving the above equations

a = 3.4 = , b = 8.5 = and

substituting the values in (1)

5x + 2y – 3z = 17

Vector equation of the plane is

The line passes through B(1, 3, – 2)

5(1) + 2(3)—3(– 2) = 17

The point B lies on the plane .

the line lies on the plane