3D Geometry
Three Dimensional Geometry
nta_pyq_2025_jan
Grade 12
Question:
Let in a △ABC , the length of the side AC be 6 , the vertex B be (1, 2, 3) and the vertices A, C lie on the line y-7 . Then the area (in sq. units) of △ABC is: x-6 z-7 = = 3 2 -2
Step-by-Step Solution
Key Concept: Apply the core result for lines and planes in three dimensions and simplify using the given constraints.
(2) Let M(3\lambda + 6, 2\lambda + 7, -2\lambda + 7) - -\to ^ ^ ^ BM = (3\lambda + 5) i + (2\lambda + 5) j + (-2\lambda + 4)k - -\to - -\to AC ⋅ BM = 0 = 3(3\lambda + 5) + 2(2\lambda + 5) - 2(-2\lambda + 4) - -\to ^ ^ ^ BM = 2 i + 3 j + 6k - -\to ∣ BM = 7 1 Area = \times 6 \times 7 = 21 2
Correct Answer: 2