Three Dimension...

If foot of the perpendicular from B(-2, 1, 4) to plane is (3, 1, 2). Then, the equation of the plane is

If θ is the angle between the planes 2x - y + z - 1 = 0 and x - 2y + z + 2 = 0, then cos θ is equal to

The plane 2λx - (1 + λ)y + 3z = 0 passes through the intersection of the planes

The reflection of the plane 2x - 3y + 4z - 3 = 0 in the plane x - y + z - 3 = 0 is the plane

The equation of plane passing through a point A(2, -1, 3) and parallel to the vectors a = (3, 0, -1) and b = (-3, 2, 2) is

The points A(4, 5, 1), B(0, -1, -1), C(3, 9, 4) and D(-4, 4, 4) are

The equation of the plane which the axes in A, B, C such that the centroid of ∆ABC is

If O is the origin and A is the point (a, b, c), then the equation of the plane through A and right angles to OA is

The image of the point (5, 4, 6) in the plane x + y + 2z - 15 = 0 is

The equation of the plane through the point (1, 2, 3) and parallel to the plane x + 2y + 5z = 0 is