If $$\theta_1, \theta_2$$ and $$\theta_3$$ are the angles made by a line with the positive direction of $$X, Y$$ and $$Z$$-axes, then $$\cos 2 \theta_1+\cos 2 \theta_2+\cos 2 \theta_3$$ is equal to

The image of the point $$(2,-3,4)$$ with respect to the plane $$4 x+2 y-4 z+3=0$$, is

If a variable plane cuts the coordinate axes in $$A, B, C$$ and is at constant distance $p$ from the origin, then the locus of the centroid of the tetrahedron $$A B C$$ is equal to

A force of magnitude $$\sqrt{6}$$ acting along, the line joining points $$A(2,-1,1)$$ and $$B(3,1,2)$$ displaces a particle from $$A$$ to $$B$$. The work done by the force is