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  • Using vectors, find the area of the triangle ABC with vertices A (1, 2, 3), B(2, –1, 4) and C (4, 5, – 1).  

Using vectors, find the area of the triangle ABC with vertices A (1, 2, 3), B(2, –1, 4) and C (4, 5, – 1).

 

Answers (1)

\\ AB=\hat{i}-3 \hat{j}+\hat{k} \\ B C=2 \hat{i}+6 j-5 \hat{k}\\ AB \times B C=9 \hat{i}+7 \hat{j}+12 \hat{k}\\

|AB \times BC | = \sqrt{81+49+144}= \sqrt{274} \\

\\ \text { Area of } \Delta A B C=\frac{1}{2} \mid AB \times BC | =\frac{1}{2} \sqrt{274} \\

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