Find the equation of the plane passing through the origin and perpendicular to each of the planes x + 2y - z = 1 and 3x - 4y + z = 5.
Applying condition of perpendicularity between planes,
Where A, B, C are direction ratios of plane and A1, B1, C1 are of other
plane.
(1)
(2)
And plane passes through (0, 0, 0),
A(x-0) + B(y-0) + C(z-0)=0
Ax + By + Cz=0 (3)
On solving equation (1) and (2)
Putting values in equation(3)
B(x + 2y + 5z)=0
x + 2y + 5z=0
So, required equation of plane is x + 2y + 5z=0.
1