TS EAMCET · Maths · Three Dimensional Geometry
The number of values of ' \(k\) ' for which the points \((-4,9, k),(-1,6, k),(0,7,10)\) form a right-angled isosceles triangle is
- A 0
- B 1
- C 2
- D 4
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\(AB^2 = (-1 - (-4))^2 + (6 - 9)^2 + (k - k)^2 = 3^2 + (-3)^2 + 0^2 = 18\) \(BC^2 = (0 - (-1))^2 + (7 - 6)^2 + (10 - k)^2 = 1^2 + 1^2 + (10 - k)^2 = 2 + (10 - k)^2\) \(AC^2 = (0 - (-4))^2 + (7 - 9)^2 + (10 - k)^2 = 4^2 + (-2)^2 + (10 - k)^2 = 20 + (10 - k)^2\)…
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