Question

If the extremities of the 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

(b) $\sqrt{3}$

Length of the diagonal = $\sqrt{{\left(2-1\right)}^2+{\left(-3+2\right)}^2+{\left(5-3\right)}^2}=\sqrt{1+1+4}=\sqrt{6}$

∴ Length of the side = $\frac{\mathrm{Length}\mathrm{of}\mathrm{diagonal}}{\sqrt{2}}=\frac{\sqrt{6}}{\sqrt{2}}=\sqrt{3}$