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JEE Main & Advanced Mathematics Vector Algebra Question Bank Self Evaluation Test - Vector Algebra

  • question_answer
    The adjacent sides AB and AC of a triangle ABC are represented by the vectors \[-2\hat{i}+3\hat{j}+2\hat{k}\]  and \[-4\hat{i}+5\hat{j}+2\hat{k}\] respectively. The area of the triangle ABC is

    A) 6 square units

    B) 5 square units

    C) 4 square units

    D) 3 square units

    Correct Answer: D

    Solution :

    [d] Area of \[\Delta \,ABC=\frac{1}{2}\left( \overrightarrow{AB}\times \overrightarrow{AC} \right)\] \[=\frac{1}{2}\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    -2 & 3 & 2  \\    -4 & 5 & 2  \\ \end{matrix} \right|\] \[=\frac{1}{2}\left[ \hat{i}(6-10)-\hat{j}(-4+8)+\hat{k}(-10+12) \right]\] \[=\frac{1}{2}\left[ -4\hat{i}-4\hat{j}+2\hat{k} \right]\] \[=\frac{1}{2}\sqrt{16+16+4}=\frac{1}{2}\sqrt{36}\] \[=\frac{1}{2}\times 6\] \[=3\] square units


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