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Manipal Engineering Manipal Engineering Solved Paper-2010

  • question_answer
    In a trapezoid of the vector\[\overset{\to }{\mathop{\mathbf{BC}}}\,=\lambda \overset{\to }{\mathop{\mathbf{AD}}}\,\]. We will, then find that\[\overset{\to }{\mathop{\mathbf{P}}}\,=\overset{\to }{\mathop{\mathbf{AC}}}\,+\overset{\to }{\mathop{\mathbf{BD}}}\,\]is collinear with\[\overset{\to }{\mathop{\mathbf{AD}}}\,\]. If\[\overset{\to }{\mathop{\mathbf{P}}}\,=\mu \overset{\to }{\mathop{\mathbf{AD}}}\,\], then

    A) \[\mu =\lambda +1\]                    

    B) \[\lambda =\mu +1\]

    C) \[\lambda +\mu =1\]    

    D)        \[\mu =2+\lambda \]

    Correct Answer: A

    Solution :

     We have,\[\overset{\to }{\mathop{\mathbf{P}}}\,=\overset{\to }{\mathop{\mathbf{AC}}}\,+\overset{\to }{\mathop{\mathbf{BD}}}\,=\overset{\to }{\mathop{\mathbf{AC}}}\,+\overset{\to }{\mathop{\mathbf{BC}}}\,+\overset{\to }{\mathop{\mathbf{CD}}}\,\] \[=\overset{\to }{\mathop{\mathbf{AC}}}\,+\lambda \overset{\to }{\mathop{\mathbf{AD}}}\,+\overset{\to }{\mathop{\mathbf{CD}}}\,=\lambda \overset{\to }{\mathop{\mathbf{AD}}}\,+(\overset{\to }{\mathop{\mathbf{AC}}}\,+\overset{\to }{\mathop{\mathbf{CD}}}\,)\] \[=\lambda \overset{\to }{\mathop{\mathbf{AD}}}\,+\overset{\to }{\mathop{\mathbf{AD}}}\,=(\lambda +1)\overset{\to }{\mathop{\mathbf{AD}}}\,\] But,\[\overset{\to }{\mathop{\mathbf{P}}}\,=\mu \overset{\to }{\mathop{\mathbf{AD}}}\,\] \[\therefore \]  \[\mu =\lambda +1\]


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