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)

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