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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 1

  • question_answer
    If the planes \[x=cy+bz,y=az+cx,z=bx+ay\] pass through a line, then \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc\] is

    A)  0                    

    B)  1    

    C)  2                    

    D) 3

    Correct Answer: B

    Solution :

    [b]: If the planes\[x-cy-bz=0\],\[-cx+y-az=0,\]\[-bx-ay+z=0\]pass through a line, then determinant formed by coefficients of unknowns is equal to zero. \[\Rightarrow \left| \begin{matrix}    1 & -c & -b  \\    -c & 1 & -a  \\    -b & -a & 1  \\ \end{matrix} \right|=0\] \[\Rightarrow 1(1-{{a}^{2}})+c(-c-ab)-b(ca+b)=0\] \[\Rightarrow 1-{{a}^{2}}-{{c}^{2}}-abc-abc-{{b}^{2}}=0\] \[\Rightarrow {{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc-1=0\] \[\Rightarrow {{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc=1\]


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