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Question
If the extremities of the diagonal of a square are (1, –2, 3 and (2, –3, 5), then the length of the side is
Options
\[\sqrt{6}\]
\[\sqrt{3}\]
\[\sqrt{5}\]
\[\sqrt{7}\]
Solution
\[\sqrt{3}\]
Length of the diagonal =
\[\sqrt{\left( 2 - 1 \right)^2 + \left( - 3 + 2 \right)^2 + \left( 5 - 3 \right)^2} = \sqrt{1 + 1 + 4} = \sqrt{6}\]
∴ Length of the side = \[\frac{\text{ Length of diagonal }}{\sqrt{2}} = \frac{\sqrt{6}}{\sqrt{2}} = \sqrt{3}\]
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