Question

If the extremities of a diagonal of a square are $(1,-2,3)$ and $(2,-3,5)$, then area of the square is

• A. $6$
• B. $3$
• C. $\frac{3}{2}$
• D. $\sqrt{3}$

Answer 1

The correct option is B $3$

Let the extremities of the diagonal of a square be $(1,-2,3)$ and $B(2,-3,5)$.
Then diagonal $AB$ is given by ${(1^2+1^2+2^2)}^{0.5}$ = $\sqrt{6}$
Hence, length of the side $=\text{length of diagonal}÷\sqrt{2}=\sqrt{3}$
So, area of square will be $\sqrt{3}\times \sqrt{3}=3$