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NDA 2022 Maths · Mathematics · Vector Algebra · hard

The area of the parallelogram whose diagonals are 3hat i+hat j-2hat k and hat i-3hat j+4hat k is

Single correct option

The area of the parallelogram whose diagonals are 3i^+j^−2k^3\hat i+\hat j-2\hat k and i^−3j^+4k^\hat i-3\hat j+4\hat k is
  1. A. 10310\sqrt3 square units
  2. B. 300\sqrt{300} square units
  3. C. 55 square units
  4. D. 535\sqrt3 square units
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Answer: (D) 535\sqrt3 square units

Area =12∣d⃗1×d⃗2∣=\frac12|\vec d_1\times\vec d_2|. Cross product =−2i^−14j^−10k^=-2\hat i-14\hat j-10\hat k with magnitude 300=103\sqrt{300}=10\sqrt3. Half of it is 535\sqrt3. Omitting 12\frac12 gives 10310\sqrt3.
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