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NDA 2 2025 Maths, question 68

Topic: Vectors

Q68

What is the area of the parallelogram whose sides are represented by the vectors i^+2j^+3k^\hat{i}+2\hat{j}+3\hat{k} and 2i^+j^+2k^2\hat{i}+\hat{j}+2\hat{k}?

  1. (a) 1226 square units\frac{1}{2}\sqrt{26}\text{ square units}
  2. (b) 1227 square units\frac{1}{2}\sqrt{27}\text{ square units}
  3. (c) 26 square units\sqrt{26}\text{ square units}Correct answer
  4. (d) 27 square units\sqrt{27}\text{ square units}

Solution.

Answer: (c) 26 square units\sqrt{26}\text{ square units}

  1. The cross product (1,2,3)×(2,1,2)=(1,4,−3).
  2. Its length is √(1+16+9)=√26, the parallelogram’s area.
  3. The factor 1/2 would apply to a triangle, not this parallelogram.