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Mathematics - Vector Question with Solution | TestHub

MathematicsVectorTetrahedron GeometryHard2 minQB

MathematicsHardsingle choice

Passage / Comprehension

Consider a tetrahedron PQRS with PQ = 4 units. A plane P1 is perpendicular to PQ. P', R' and S' are the feet of perpendiculars from P, R and S to P1, and area of triangle P'R'S' is 15 sq. units.

Volume of the tetrahedron PQRS (in cu. units) is -

Options:

Answer:

Solution:

Take $P = (0, 0, 0), Q = (0, 0, 4), R = (0, b, c), S = (p, q, r)$ . Since $\frac{1}{2} b p = 15$ , $b p = 30$ . The tetrahedron volume is $\frac{1}{3} \cdot \frac{1}{2} (4 b) \cdot p = 20$ cubic units.

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Tetrahedron Geometry

⏱ 2mℹ️ Source: QB

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