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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Vector Algebra

NDA 2012 · Mathematics · Vector Algebra

What is the area of the rectangle having vertices A, B , C and D...

What is the area of the rectangle having vertices A,B\mathrm{A}, \mathrm{B}, C and D with position vectors −i^+12j^+4k^-\hat{i}+\frac{1}{2} \hat{j}+4 \hat{k}, i^+12j^+4k^,i^−12j^+4k^\hat{i}+\frac{1}{2} \hat{j}+4 \hat{k}, \hat{i}-\frac{1}{2} \hat{j}+4 \hat{k} and −i^−12j^+4k^-\hat{i}-\frac{1}{2} \hat{j}+4 \hat{k} ?

Options

  1. A1/2 square unit
  2. B1 square unit
  3. C2 square unit
  4. D4 square unit

Correct answer

B. 1 square unit

Step-by-step solution

A(−1,12,4)B(1,12,4)B(−1,12,4)C(1,−12,4)\begin{aligned} & \mathrm{A}\left(-1, \frac{1}{2}, 4\right) \mathrm{B}\left(1, \frac{1}{2}, 4\right) \\ & \mathrm{B}\left(-1, \frac{1}{2}, 4\right) \mathrm{C}\left(1, \frac{-1}{2}, 4\right) \end{aligned}\mathrm{AB}=1 \mathrm{BC}=1$ Area (1).
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