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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

What is the area of the triangle whose vertices are (0,0,0),(1,2,3)...

What is the area of the triangle whose vertices are (0,0,0),(1,2,3)(0,0,0),(1,2,3) and (−3,−2,1)(-3,-2,1) ?

Options

  1. A353 \sqrt{5} square unit
  2. B656 \sqrt{5} square unit
  3. C66 square unit
  4. D1212 square unit

Correct answer

A. 353 \sqrt{5} square unit

Step-by-step solution

Area =\frac{1}{2}|\overrightarrow{\mathrm{AB}} \times \overrightarrow{\mathrm{AC}}|=\frac{1}{2}\left|ijk123−3−21\begin{array}{ccc}i & j & k \\ 1 & 2 & 3 \\ -3 & -2 & 1\end{array}\right|
=12(8i^−10j^+4k^)=1264+16+100\begin{aligned} & =\frac{1}{2}(8 \hat{i}-10 \hat{j}+4 \hat{k}) \\ & =\frac{1}{2} \sqrt{64+16+100}\end{aligned}=12(65)=35\begin{aligned} & =\frac{1}{2}(6 \sqrt{5}) \\ & =3 \sqrt{5}\end{aligned}$
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