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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Three Dimensional Geometry

  • question_answer
    Value of\[\lambda \] such that the line\[\frac{x-1}{2}=\frac{y-1}{3}=\frac{z-1}{\lambda }\]Is perpendicular to normal to the plane\[\vec{r}.(2\vec{i}+3\vec{j}+4\vec{k})=0\] is

    A) \[-\frac{13}{4}\]

    B) \[-\frac{17}{4}\]

    C) \[4\]

    D) None of these

    Correct Answer: A

    Solution :

    [a] Since line is parallel to the plane vector \[2\vec{i}+3\vec{j}+\lambda \vec{k}\] is perpendicular to the normal to the plane \[2\vec{i}+3\vec{j}+4\vec{k}\] \[\Rightarrow 2\times 2+3\times 3+4\lambda =0\] or \[\lambda =-\frac{13}{4}\]


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