Q. If the extremities of a diagonal of a square are $ (1,-2,3) $ and $ (2,-3,5) $ then the length of the side is
J & K CETJ & K CET 2007Introduction to Three Dimensional Geometry
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)
