Question

Two opposite vertices of a square are $(2,-3,4)$ and $(4,1,-2)$. The length of the side of the square is

• A. $\sqrt{58}$
• B. $2\sqrt{7}$
• C. $\sqrt{14}$
• D. $\sqrt{7}$

Answer 1

Answer: (B)

$2\sqrt{7}$

Length of diagonal $=$ distance between the opposite vertices of the square $=\sqrt{(2-4{)}^2+(-3-1{)}^2+(4+2{)}^2}=\sqrt{56}=d$ (say)

Hence, length of sides of square $=\frac{d}{\sqrt{2}}=\sqrt{28}=2\sqrt{7}$