If the extremities of a diagonal of a square | vedclass

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(B) Let $a$ be the length of the side of the square.Let the vertices of the diagonal be $B = (1, -2, 3)$ and $D = (2, -3, 5)$.The length of the diagon

Vedclass · Accepted Answer

$\sqrt{3}$

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(B) Let $a$ be the length of the side of the square.Let the vertices of the diagonal be $B = (1, -2, 3)$ and $D = (2, -3, 5)$.The length of the diagonal $BD$ is given by the distance formula:$BD = \sqrt{(2 - 1)^2 + (-3 - (-2))^2 + (5 - 3)^2}$$BD = \sqrt{(1)^2 + (-1)^2 + (2)^2}$$BD = \sqrt{1 + 1 + 4} = \sqrt{6}$In a square,the relationship between the side $a$ and the diagonal $d$ is $d = a\sqrt{2}$.Therefore,$a\sqrt{2} = \sqrt{6}$.$a = \frac{\sqrt{6}}{\sqrt{2}} = \sqrt{3}$.Thus,the length of the side 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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