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

  • question_answer
    If the vectors \[i+3j-2k\], \[2i-j+4k\] and \[3i+2j+xk\] are coplanar, then the value of x is                 [Karnataka CET 2000]

    A)             ? 2

    B)             2

    C)             1

    D)             3

    Correct Answer: B

    Solution :

                    Vectors \[\mathbf{i}+3\mathbf{j}-2\mathbf{k};\,\,2\mathbf{i}-\mathbf{j}+4\mathbf{k}\] and \[3\mathbf{i}+2\mathbf{j}+x\mathbf{k}\]. We know that as the vectors are coplanar, therefore \[\left| \begin{align}   & \,1\,\,\,\,3\,\,-2\, \\  & \,2\,\,-1\,\,\,4 \\  & \,3\,\,\,\,2\,\,\,\,x \\ \end{align} \right|\,=0\]Þ \[1(-x-8)-3\,(2x-12)-2\,(4+3)=0\]                 Þ \[-x-8-6x+36-14=0\] Þ \[7x=14\] Þ \[x=2\].


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