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NDA 2016 Maths · Mathematics · Vector Algebra · easy

If vec a=hat i+hat j and vec b=hat j+hat k, then |vec a×vec b| is equal to

Single correct option

If a⃗=i^+j^\vec a=\hat i+\hat j and b⃗=j^+k^\vec b=\hat j+\hat k, then ∣a⃗×b⃗∣|\vec a\times\vec b| is equal to
  1. A. 33
  2. B. 11
  3. C. 3\sqrt3
  4. D. 2\sqrt2
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Answer: (C) 3\sqrt3

a⃗×b⃗=(1⋅1−0⋅1)i^−(1⋅1−0)j^+(1⋅1−0)k^=i^−j^+k^\vec a\times\vec b=(1\cdot1-0\cdot1)\hat i-(1\cdot1-0)\hat j+(1\cdot1-0)\hat k=\hat i-\hat j+\hat k, with magnitude 3\sqrt3. 2\sqrt2 is ∣a⃗∣|\vec a| or ∣b⃗∣|\vec b|, not the cross product.
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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