If projection of any line on co-ordinate axis 3, 4, and 5, then its length is

Let d be the length of line, then projection n x-axis $=\mathrm{dl}=3$ projection on y-axis $=\mathrm{dm}=4$ and projection on z-axis $=\mathrm{dn}=5.$

Now, ${\mathrm{d}}^2\left({\mathrm{l}}^2+{\mathrm{m}}^2+{\mathrm{n}}^2\right)=50\Rightarrow {\mathrm{d}}^2\left(1\right)=50\Rightarrow \mathrm{d}=5\sqrt{2}.$