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

  • question_answer
    Let \[a=i-k,\,\,\,b=xi+j+(1-x)\,k\],\[c=yi+xj+(1+x-y)k\]. Then \[[a\,\,b\,\,c]\] depends on [IIT Screening 2001; AIEEE 2005]

    A)             Only x

    B)             Only y

    C)             Neither x nor y

    D)             Both x and y

    Correct Answer: C

    Solution :

                    \[[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]=\left| \,\begin{matrix}    1 & 0 & -1  \\    x & 1 & 1-x  \\    y & x & 1+x-y  \\ \end{matrix}\, \right|=\left| \,\begin{matrix}    1 & 0 & 0  \\    x & 1 & 1  \\    y & x & 1+x  \\ \end{matrix}\, \right|=\left| \,\begin{matrix}    1 & 1  \\    x & 1+x  \\ \end{matrix}\, \right|=1\].


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