Discussion
The projection of a line segment on the co-ordinate axes are 5, 6,8 . Then the length of the line segment is
Answer: B
The length is \(5\sqrt{5}\).
The projections of a segment on the three axes are the differences of the coordinates of its ends, so the length is the square root of the sum of their squares:
\[ \begin{aligned} L &= \sqrt{5^{2} + 6^{2} + 8^{2}} = \sqrt{125} \\ &= 5\sqrt{5} \end{aligned} \]
Adding the projections (19) or picking one of them (5 or 6) ignores that they are perpendicular components. \(6\sqrt{5}\) is \(\sqrt{180}\) and \(6\sqrt{6}\) is \(\sqrt{216}\), neither of which is the sum of the squares.
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