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NDA 2018 Maths · Mathematics · Vector Algebra · medium

If vec a=2hat i-hat k and vec b=hat i+3hat j+2hat k, then |vec a×vec b| equals

Single correct option

If a⃗=2i^−k^\vec a=2\hat i-\hat k and b⃗=i^+3j^+2k^\vec b=\hat i+3\hat j+2\hat k, then ∣a⃗×b⃗∣|\vec a\times\vec b| equals
  1. A. 70\sqrt{70}
  2. B. 50\sqrt{50}
  3. C. 10\sqrt{10}
  4. D. 7070
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Answer: (A) 70\sqrt{70}

a⃗×b⃗=∣i^j^k^20−1132∣=3i^−5j^+6k^\vec a\times\vec b=\begin{vmatrix}\hat i&\hat j&\hat k\\2&0&-1\\1&3&2\end{vmatrix}=3\hat i-5\hat j+6\hat k, with magnitude 9+25+36=70\sqrt{9+25+36}=\sqrt{70}. The value 70 is the square, and 50\sqrt{50} comes from losing the sign of the j^\hat j cofactor.
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Original question written in the NDA 2018 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