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JEE Main 2016 · Mathematics · Vector Algebra · medium

The area of the triangle with adjacent sides vec a=hat i+2hat j-hat k and vec b=2hat i-hat j+hat k is

Single correct option

The area of the triangle with adjacent sides a⃗=i^+2j^−k^\vec a=\hat i+2\hat j-\hat k and b⃗=2i^−j^+k^\vec b=2\hat i-\hat j+\hat k is
  1. A. 35\sqrt{35} square units
  2. B. 62\tfrac{\sqrt{6}}{2} square units
  3. C. 352\tfrac{\sqrt{35}}{2} square units
  4. D. 112\tfrac{\sqrt{11}}{2} square units
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Answer: (C) 352\tfrac{\sqrt{35}}{2} square units

a⃗×b⃗=∣i^j^k^12−12−11∣=i^−3j^−5k^\vec a\times\vec b=\begin{vmatrix}\hat i&\hat j&\hat k\\1&2&-1\\2&-1&1\end{vmatrix}=\hat i-3\hat j-5\hat k, with magnitude 1+9+25=35\sqrt{1+9+25}=\sqrt{35}. The triangle has half this area, 352\tfrac{\sqrt{35}}2.
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Original question written in the JEE Main 2016 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake