NDA 2025 · PYQ · 3D Geometry · easy
ABC is a triangle right-angled at B. If A(k, 1, -1), B(2k, 0, 2) and C(2+2k, k, 1) are the vertices of the triangle, then what is the value of k?
- A.-3
- B.-1
- C.1✓ Correct
- D.3
BA = (k-2k, 1-0, -1-2) = (-k, 1, -3). BC = (2+2k-2k, k-0, 1-2) = (2, k, -1). Perpendicular: BA·BC = -2k + k + 3 = -k + 3 = 0, so k = 3.
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