One vertex of a rectangular parallelepiped is at the origin O and the lengths of its edges along x, y and z ax…

Question

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

A
$\frac{12}{5\sqrt{5}}$
B
$12\sqrt{5}$
C
$\frac{12}{5}$
D
$\frac{12}{\sqrt{5}}$

Accepted Answer

C. $$\frac{12}{5}$$

Answer

A. $$\frac{12}{5\sqrt{5}}$$

Answer

B. $$12\sqrt{5}$$

Answer

D. $$\frac{12}{\sqrt{5}}$$

Answer & step-by-step solution

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