If the extremities of a diagonal of a square | vedclass

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(B) Let the side of the square be $a$.The length of the diagonal $d$ of a square with side $a$ is given by $d = a\sqrt{2}$.The distance between the tw

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$\sqrt{3}$

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(B) Let the side of the square be $a$.The length of the diagonal $d$ of a square with side $a$ is given by $d = a\sqrt{2}$.The distance between the two given points $(1, -2, 3)$ and $(2, -3, 5)$ is the length of the diagonal $d$.$d = \sqrt{(2-1)^2 + (-3 - (-2))^2 + (5-3)^2}$$d = \sqrt{(1)^2 + (-1)^2 + (2)^2}$$d = \sqrt{1 + 1 + 4} = \sqrt{6}$Since $d = a\sqrt{2}$, we have:$a\sqrt{2} = \sqrt{6}$$a = \frac{\sqrt{6}}{\sqrt{2}} = \sqrt{3}$Therefore, the length of the side of the square is $\sqrt{3}$.

If the extremities of a diagonal of a square are $(1, -2, 3)$ and $(2, -3, 5)$, then the length of its side is

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