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

Question

Aicharya · Accepted Answer

Let side of the square is $a$

Then, the length of the diagonal $A C=a \sqrt{2}$. Also, length of the diagonal $\begin{array}{r}A C=\sqrt{(1-2)^2+(-2+3)^2+(3-5)^2} \\ =\sqrt{1+1+4}=\sqrt{6} \\ \text { Thus, } \quad a \sqrt{2}=\sqrt{6} \Rightarrow a=\sqrt{3}\end{array}$

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

Solution