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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Critical Thinking

  • question_answer
    The points \[A(4,\,5,\,1),B(0,-1,-1),C(3,\,9,\,4)\]and \[D(-4,\,4,\,4)\]are [Kurukshetra CEE 2002]

    A) Collinear

    B) Coplanar

    C) Non- coplanar

    D) Non- Collinear and non-coplanar

    Correct Answer: B

    Solution :

    • \[AB\equiv (-4,\,-6,\,-2);\] \[AC\equiv (-1,\,4,\,3)\];  \[AD\equiv (-8,\,-1,\,3)\]                   
    • Points A, B, C, D are coplaner, if \[[\overrightarrow{AB},\,\overrightarrow{AC},\,\overrightarrow{AD}]=0\]                   
    • Þ \[\left| \,\begin{matrix}    -4 & -6 & -2  \\    -1 & 4 & 3  \\    -8 & -1 & 3  \\ \end{matrix}\, \right|\,=\,0\].


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