JEE Math Practice Question

One vertex of a rectangular parallelopiped is at the origin $$\mathrm{O}$$ and the lengths of its edges along $$x, y$$ and $$z$$ axes are $$3,4$$ and $$5$$ units respectively. Let $$\mathrm{P}$$ be the vertex $$(3,4,5)$$. Then the shortest distance between the diagonal OP and an edge parallel to $$\mathrm{z}$$ axis, not passing through $$\mathrm{O}$$ or $$\mathrm{P}$$ is :

1. A.$$\frac{12}{\sqrt{5}}$$
2. B.$$12 \sqrt{5}$$
3. C.$$\frac{12}{5}$$
4. D.$$\frac{12}{5 \sqrt{5}}$$