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(C) Let the length of the line segment be $L$ and the angles it makes with the $x, y,$ and $z$ axes be $\alpha, \beta,$ and $\gamma$ respectively.The

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$5\sqrt{2}$

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(C) Let the length of the line segment be $L$ and the angles it makes with the $x, y,$ and $z$ axes be $\alpha, \beta,$ and $\gamma$ respectively.The projections of the line segment on the coordinate axes are given by $L \cos \alpha = 3$,$L \cos \beta = 4$,and $L \cos \gamma = 5$.Squaring and adding these equations,we get:$(L \cos \alpha)^2 + (L \cos \beta)^2 + (L \cos \gamma)^2 = 3^2 + 4^2 + 5^2$$L^2 (\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma) = 9 + 16 + 25$Since $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$,we have:$L^2 (1) = 50$$L = \sqrt{50} = 5\sqrt{2}$.

The projection of a line segment on the coordinate axes are $3, 4,$ and $5$ respectively. Find the length of the line segment.

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