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NDA 2022 Maths · Mathematics · Vector Algebra · medium

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

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If a⃗=i^+2j^+2k^\vec a=\hat i+2\hat j+2\hat k and b⃗=2i^+j^−2k^\vec b=2\hat i+\hat j-2\hat k, then ∣a⃗×b⃗∣|\vec a\times\vec b| is
  1. A. 00
  2. B. 33
  3. C. 45\sqrt{45}
  4. D. 99
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Answer: (D) 99

a⃗×b⃗=(−4−2)i^−(−2−4)j^+(1−4)k^=−6i^+6j^−3k^\vec a\times\vec b=(-4-2)\hat i-(-2-4)\hat j+(1-4)\hat k=-6\hat i+6\hat j-3\hat k, magnitude 36+36+9=9\sqrt{36+36+9}=9. Note a⃗⋅b⃗=0\vec a\cdot\vec b=0 but that does not make the cross product zero.
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