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JCECE Engineering JCECE Engineering Solved Paper-2012

  • question_answer
    If the planes\[x-cy-bz=0\], \[ex-y+az=0\] and\[bx+ay-z=0\], pass through a line, then find the value of\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc\].

    A) \[0\]                                     

    B) \[1\]

    C) \[-1\]                                    

    D) \[\frac{1}{2}\]

    Correct Answer: B

    Solution :

    Given, planes are                 \[x-cy-bz=0\]                                  ... (i)                 \[ex-y+az=0\]                                ... (ii)                 \[bx+ay-z=0\]                                ... (iii) Equation of plane passing through the line of intersection of planes (i) and (ii) may be taken as \[(x-cy-bz)+\lambda (cx-y+az)=0\]                 \[(1+c\lambda )x+y(-c-\lambda )+z(-b+a\lambda )=0\] ... (iv) Now, planes (iii) and (iv) are same. \[\therefore \]  \[\frac{1+c\lambda }{b}=\frac{-(c+\lambda )}{a}=\frac{-b+a\lambda }{-1}\] By eliminating\[\lambda \], we get                 \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc=1\]


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