Question

The three points A (1, 2, 3), B (3, 1, 2), C (2, 3, 1) form ________________

(a) equilateral triangle

(b) right angled triangle

(c) isosceles triangle

(d) right angled isosceles triangle

This question was posed to me in quiz.

Origin of the question is Three Dimensional Geometry topic in division Three Dimensional Geometry of Mathematics – Class 11

Answer 1

Right option is (a) equilateral triangle

Easy explanation: We know, distance between two points (x1, y1, z1) and (x2, y2, z2) is \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}\).

Distance AB = \(\sqrt{(1-3)^2+(2-1)^2+(3-2)^2} = \sqrt{6}\)

Distance BC = \(\sqrt{(3-2)^2+(1-3)^2+(2-1)^2} = \sqrt{6}\)

Distance CA = \(\sqrt{(2-1)^2+(3-2)^2+(1-3)^2} = \sqrt{6}\)

Since AB=BC=CA so, it forms equilateral triangle.