Question

The points $ A(-1, 2, 3), B(2, -3, 1), C(3, 1, -2) $ are:

• A. are collinear
• B. form an isosceles triangle
• C. form a right angled triangle
• D. form a scalene triangle

Hint:

Use distance formula for three points to check side lengths and classify the triangle.

Answer 1

The Correct Option is D

Calculate lengths of sides: \[ AB = \sqrt{(2+1)^2 + (-3-2)^2 + (1-3)^2} = \sqrt{3^2 + (-5)^2 + (-2)^2} = \sqrt{9 + 25 + 4} = \sqrt{38} \] \[ BC = \sqrt{(3-2)^2 + (1+3)^2 + (-2-1)^2} = \sqrt{1^2 + 4^2 + (-3)^2} = \sqrt{1 + 16 + 9} = \sqrt{26} \] \[ CA = \sqrt{(-1-3)^2 + (2-1)^2 + (3+2)^2} = \sqrt{(-4)^2 + 1^2 + 5^2} = \sqrt{16 + 1 + 25} = \sqrt{42} \] Since all sides are different, triangle is scalene.