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If the extremities of diagonal of a square $(1,-2,3),(2,-3,5)$, then the length of its side, is
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The correct answer is:
$\sqrt{3}$
Let side of the square is $a$
Then, the length of the diagonal $A C=a \sqrt{2}$.
Also, length of the diagonal
$\begin{array}{r}A C=\sqrt{(1-2)^2+(-2+3)^2+(3-5)^2} \\ =\sqrt{1+1+4}=\sqrt{6} \\ \text { Thus, } \quad a \sqrt{2}=\sqrt{6} \Rightarrow a=\sqrt{3}\end{array}$
Then, the length of the diagonal $A C=a \sqrt{2}$.
Also, length of the diagonal
$\begin{array}{r}A C=\sqrt{(1-2)^2+(-2+3)^2+(3-5)^2} \\ =\sqrt{1+1+4}=\sqrt{6} \\ \text { Thus, } \quad a \sqrt{2}=\sqrt{6} \Rightarrow a=\sqrt{3}\end{array}$
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