Question

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. $\sqrt{7}$

Answer 1

Answer: (B)

$\sqrt{3}$

Answer 2

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)