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

Question

Philoid · Accepted Answer

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