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NDA 2016 Maths · Mathematics · Vector Algebra · hard

The area of the triangle with vertices A(1,0,0), B(0,1,0) and C(0,0,1) is

Single correct option

The area of the triangle with vertices A(1,0,0)A(1,0,0), B(0,1,0)B(0,1,0) and C(0,0,1)C(0,0,1) is
  1. A. 32\dfrac{\sqrt3}{2} square units
  2. B. 3\sqrt3 square units
  3. C. 12\dfrac12 square units
  4. D. 32\dfrac32 square units
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Answer: (A) 32\dfrac{\sqrt3}{2} square units

AB⃗=(−1,1,0)\vec{AB}=(-1,1,0), AC⃗=(−1,0,1)\vec{AC}=(-1,0,1), and AB⃗×AC⃗=(1,1,1)\vec{AB}\times\vec{AC}=(1,1,1). Area =123=\tfrac12\sqrt3. Omitting the 12\tfrac12 gives 3\sqrt3, which is the area of the parallelogram.
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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