Question

The three points A (3, 0, 3), B (5, 3, 2), C (6, 5, 5) form ________________

(a) equilateral triangle

(b) right angled triangle

(c) isosceles triangle

(d) right angled isosceles triangle

This question was addressed to me in an online interview.

Question is taken from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 11

Answer 1

Right choice is (c) isosceles triangle

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 = \(\sqrt{(3-5)^2+(0-3)^2+(3-2)^2} = \sqrt{14}\)

Distance BC =\(\sqrt{(5-6)^2+(3-5)^2+(2-5)^2} = \sqrt{14}\)

Distance AC =\(\sqrt{(3-6)^2+(0-5)^2+(3-5)^2} = \sqrt{38}\)

Since AB =BC so, it forms isosceles triangle.