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NDA 2017 Maths · Mathematics · Vector Algebra · hard

Three concurrent edges of a tetrahedron are hat i+2hat j, hat j+2hat k and 2hat i+hat k. Its volume is

Single correct option

Three concurrent edges of a tetrahedron are i^+2j^, j^+2k^\hat i+2\hat j,\ \hat j+2\hat k and 2i^+k^2\hat i+\hat k. Its volume is
  1. A. 32\frac32 cubic units
  2. B. 99 cubic units
  3. C. 94\frac94 cubic units
  4. D. 92\frac92 cubic units
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Answer: (A) 32\frac32 cubic units

The scalar triple product is ∣120012201∣=1(1)−2(0−4)+0=9\begin{vmatrix}1&2&0\\0&1&2\\2&0&1\end{vmatrix}=1(1)-2(0-4)+0=9. A tetrahedron has one-sixth of the parallelepiped's volume, so V=96=32V=\frac96=\frac32. The value 99 is the parallelepiped volume and 92\frac92 uses one-half.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake