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NDA 2020 Maths · Mathematics · Vector Algebra · medium

The volume of the parallelepiped whose coterminous edges are vec a=hat i+2hat j-hat k, vec b=3hat i+2hat k and vec c=-2hat i+hat j+hat k is

Single correct option

The volume of the parallelepiped whose coterminous edges are a⃗=i^+2j^−k^\vec a=\hat i+2\hat j-\hat k, b⃗=3i^+2k^\vec b=3\hat i+2\hat k and c⃗=−2i^+j^+k^\vec c=-2\hat i+\hat j+\hat k is
  1. A. −19-19
  2. B. 1717
  3. C. 1919
  4. D. 1313
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Answer: (C) 1919

The volume is ∣[a⃗ b⃗ c⃗]∣|[\vec a\ \vec b\ \vec c]|. Expanding the determinant ∣12−1302−211∣\begin{vmatrix}1&2&-1\\3&0&2\\-2&1&1\end{vmatrix} along the first row: 1(0−2)−2(3+4)+(−1)(3−0)=−2−14−3=−191(0-2)-2(3+4)+(-1)(3-0)=-2-14-3=-19. A volume cannot be negative, so it is ∣−19∣=19|-19|=19. The option −19-19 is the signed triple product, which only gives the orientation of the three vectors.
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