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

  • question_answer
    \[a=i+j+k,\,\mathbf{b}=2i-4k,\,c=i+\lambda \,j+3k\] are coplanar, then the value of \[\lambda \] is [MP PET 2000]

    A)             5/2

    B)             3/5

    C)             7/3

    D)             None of these

    Correct Answer: D

    Solution :

                    \[\because \]\[a=i+j+k\],\[b=2i-4k,\,c=i+\lambda \,j+3k\]arec oplanar.                    \\[[a\,b\,c]=0\]\[\Rightarrow \,\,\,\left| \,\begin{matrix}    1 & 1 & 1  \\    2 & 0 & -4  \\    1 & \lambda  & 3  \\ \end{matrix}\, \right|\,=0\]                                 \[\Rightarrow 4\lambda -\left( 6+4 \right)+2\lambda =0\]                                 Þ \[6\lambda =10\,\,\,\Rightarrow \lambda =\frac{5}{3}\].


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