AP EAMCET · Maths · Three Dimensional Geometry
The points \(\mathrm{A}(-1,2,3), \mathrm{B}(2,-3,1), \mathrm{C}(3,1,-2)\)
- A are collinear
- B form an isosceles triangle
- C form a right angled triangle
- D form a scalene triangle
Answer & Solution
Correct Answer
(D) form a scalene triangle
Step-by-step Solution
Detailed explanation
\( AB^2 = (2 - (-1))^2 + (-3 - 2)^2 + (1 - 3)^2 = 3^2 + (-5)^2 + (-2)^2 = 9 + 25 + 4 = 38 \) \( BC^2 = (3 - 2)^2 + (1 - (-3))^2 + (-2 - 1)^2 = 1^2 + 4^2 + (-3)^2 = 1 + 16 + 9 = 26 \) \( AC^2 = (3 - (-1))^2 + (1 - 2)^2 + (-2 - 3)^2 = 4^2 + (-1)^2 + (-5)^2 = 16 + 1 + 25 = 42 \)…
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