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

If $$(3,4,-1)$$ and $$(-1,2,3)$$ be end points of the diameter of a sphere, then the radius of the sphere is

The following lines are

$$\begin{aligned} \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda^{\prime}(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}), \\ \text { and } \quad \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}) \end{aligned}$$