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JEE Main & Advanced Mathematics Vector Algebra Question Bank Application of vectors in three dimensional geometry

  • question_answer
    The distance between the line \[\mathbf{r}=2\mathbf{i}-2\mathbf{j}+3\mathbf{k}+\lambda (\mathbf{i}-\mathbf{j}+4\mathbf{k})\] and the plane \[\mathbf{r}.(\mathbf{i}+5\mathbf{j}+\mathbf{k})=5\] is [AIEEE 2005]

    A)            \[\frac{3}{10}\]

    B)            \[\frac{10}{3}\]

    C)            \[\frac{10}{9}\]

    D)            \[\frac{10}{3\sqrt{3}}\]

    Correct Answer: D

    Solution :

               Required distance \[=\left. \left| \frac{d-\mathbf{a}.\mathbf{n}}{|\mathbf{n}|} \right. \right|=\left. \left| \frac{5-(2\mathbf{i}-2\mathbf{j}+3\mathbf{k}).(\mathbf{i}+5\mathbf{j}+\mathbf{k})}{\sqrt{1+25+1}} \right. \right|\]                                                                       \[\left. =\left| \frac{5-(2-10+3)}{\sqrt{27}} \right. \right|\]\[=\frac{10}{3\sqrt{3}}\].


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