question_answer

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

A)  \[\sqrt{6}\]       

B)  \[\sqrt{3}\]

C)  \[\sqrt{5}\]           

D)  \[\sqrt{7}\]

Correct Answer: B

Solution :

Length of the diagonal \[AB=\sqrt{{{(1-2)}^{2}}+{{(-2+3)}^{2}}+{{(3-5)}^{2}}}\] \[=\sqrt{1+1+4}=\sqrt{6}\] Now.   \[A{{C}^{2}}+B{{C}^{2}}=A{{B}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{x}^{2}}={{(\sqrt{6})}^{2}}\] \[\Rightarrow \] \[2{{x}^{2}}=6\] \[\Rightarrow \] \[{{x}^{2}}=3\] \[\Rightarrow \] \[x=\sqrt{3}\] (\[\because \] length cannot be negative)