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NDA 2016 Maths · Mathematics · Vector Algebra · hard

The volume of the parallelepiped with edges hat i+2hat j, hat j+3hat k and 2hat i+hat k is

Single correct option

The volume of the parallelepiped with edges i^+2j^\hat i+2\hat j, j^+3k^\hat j+3\hat k and 2i^+k^2\hat i+\hat k is
  1. A. −13-13 cubic units
  2. B. 1111 cubic units
  3. C. 1515 cubic units
  4. D. 1313 cubic units
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Answer: (D) 1313 cubic units

Volume =∣a⃗⋅(b⃗×c⃗)∣=|\vec a\cdot(\vec b\times\vec c)|, the absolute value of the determinant with rows (1,2,0),(0,1,3),(2,0,1)(1,2,0),(0,1,3),(2,0,1). Expanding: 1(1)−2(0−6)+0=131(1)-2(0-6)+0=13. Volume cannot be negative, so −13-13 is rejected.
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Original question written in the NDA 2016 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