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JEE Main & Advanced Mathematics Vector Algebra Question Bank Scalar triple product and their applications

  • question_answer
    If the vectors \[4i+11j+mk,\,7i+2j+6k\] and \[i+5j+4k\] are coplanar, then m is                            [Karnataka CET 2003]

    A)             38

    B)             0

    C)             10

    D)             ? 10

    Correct Answer: C

    Solution :

                    \[\because \] The vectors \[4\mathbf{i}+11\mathbf{j}+m\mathbf{k},\,7\mathbf{i}+2\mathbf{j}+6\mathbf{k}\] and \[\mathbf{i}+5\mathbf{j}+4\mathbf{k}\] are coplanar.                                 \[\therefore \,\left| \,\begin{matrix}    4 & 11 & m  \\    7 & 2 & 6  \\    1 & 5 & 4  \\ \end{matrix}\, \right|=0\]                                 \[\Rightarrow 4(8-30)-11(28-6)+m\,(35-2)=0\]                                 \[\Rightarrow -88-11\times 22+33m=0\]\[\Rightarrow -8-22+3m=0\]                                 \[\Rightarrow 3m=30\] \[\Rightarrow m=10.\]


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