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NDA 2020 Maths · Mathematics · Vector Algebra · easy

The area of the parallelogram having adjacent sides vec a=hat i+2hat j and vec b=3hat i-hat j is

Single correct option

The area of the parallelogram having adjacent sides a⃗=i^+2j^\vec a=\hat i+2\hat j and b⃗=3i^−j^\vec b=3\hat i-\hat j is
  1. A. 55
  2. B. 11
  3. C. 66
  4. D. 77
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Answer: (D) 77

The area is ∣a⃗×b⃗∣|\vec a\times\vec b|. For vectors in the xy-plane, a⃗×b⃗=(1⋅(−1)−2⋅3)k^=−7k^\vec a\times\vec b=(1\cdot(-1)-2\cdot3)\hat k=-7\hat k, so the area is 77. The negative sign only gives the direction and must be dropped through the modulus. The value 11 is a⃗⋅b⃗=3−2\vec a\cdot\vec b=3-2, the scalar product, and 55 is ∣a⃗∣2=1+4|\vec a|^2=1+4, a number that has nothing to do with the cross product.
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Original question written in the NDA 2020 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