Question

A rod of length 2 units whose one end is (1, 0, -) and other end touches the plane x - 2y + 2z + 4 = 0, is rotated on this plane, then 

(A) the rod sweeps a solid structure whose volume is π cubic units

(B) the area of the region which the rod traces on the plane is 2π

(C) the length of projection of the rod on the plane is √3 units

(D) the centre of the region which the rod traces on the plane is (2/3, 2/3,-5/3)

Answer 1

Correct option (A)(C)(D)

Explanation:

The rod sweeps out the figure which is a cone. The distance of point (A(1, 0, - 1) from the plane is 1 + 1 -2 + 4/√ 9 = 1 unit.

The slant height l of the cone is 2 units. Then the radius of the base of the cone is

Hence, the volume of the cone is

π/3(√3)².1 = π cubic units.

Area of the circle on the plane which the rod traces is 3π.

Also, the centre of the circle is Q(x, y, z). Then