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NDA 2024 Maths · Mathematics · Vector Algebra · medium

The area of the triangle with vertices at the origin, 2hat i+hat j and hat i+3hat j is

Single correct option

The area of the triangle with vertices at the origin, 2i^+j^2\hat i+\hat j and i^+3j^\hat i+3\hat j is
  1. A. 55 square units
  2. B. 72\frac72 square units
  3. C. 12\frac12 square units
  4. D. 52\frac52 square units
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Answer: (D) 52\frac52 square units

Area =12∣a⃗×b⃗∣=12∣2⋅3−1⋅1∣=52=\frac12|\vec a\times\vec b|=\frac12|2\cdot3-1\cdot1|=\frac52. Trap: omitting the factor 12\frac12 gives 5 (the parallelogram), and adding the products (2⋅3+1⋅1=72\cdot3+1\cdot1=7) instead of subtracting is the dot product mistake, producing 72\frac72.
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