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JEE Main 2019 · Mathematics · Vector Algebra · medium

A parallelogram is formed with vec a=hat i+2hat j+3hat k and vec b=2hat i-hat j+hat k as two adjacent sides. Its area is

Single correct option

A parallelogram is formed with a⃗=i^+2j^+3k^\vec a=\hat i+2\hat j+3\hat k and b⃗=2i^−j^+k^\vec b=2\hat i-\hat j+\hat k as two adjacent sides. Its area is
  1. A. 535\sqrt3
  2. B. 3
  3. C. 5
  4. D. 2212\sqrt{21}
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Answer: (A) 535\sqrt3

a⃗×b⃗=(2⋅1−3(−1))i^−(1⋅1−3⋅2)j^+(1(−1)−2⋅2)k^=5i^+5j^−5k^\vec a\times\vec b=(2\cdot1-3(-1))\hat i-(1\cdot1-3\cdot2)\hat j+(1(-1)-2\cdot2)\hat k=5\hat i+5\hat j-5\hat k. Its magnitude is 535\sqrt3, which is the area. (Note ∣a⃗∣∣b⃗∣=221|\vec a||\vec b|=2\sqrt{21} is not the area.)
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