AMU Medical AMU Solved Paper-2008

  • question_answer
    The value of P so that the vectors \[2\overset{\hat{\ }}{\mathop{i}}\,-\overset{\hat{\ }}{\mathop{j}}\,+\overset{\hat{\ }}{\mathop{k}}\,,\]\[\overset{\hat{\ }}{\mathop{i}}\,+\overset{\hat{\ }}{\mathop{2j}}\,-\overset{\hat{\ }}{\mathop{3k}}\,,\]and \[3\overset{\hat{\ }}{\mathop{i}}\,+\overset{\hat{\ }}{\mathop{pj}}\,+\overset{\hat{\ }}{\mathop{5k}}\,,\] are coplanar should be

    A)  16                                         

    B)  -4

    C)  4                                            

    D)  -8

    Correct Answer: B

    Solution :

                     For coplanarity                                 \[\left| \begin{matrix}    2 & -1 & 1  \\    1 & 2 & -3  \\    3 & P & 5  \\ \end{matrix} \right|=0\]                 2 (10 + 3P) + 1(5 + 9) + 1(P - 6) = 0                 20 + 6P + 5 + 9 + P - 6 = 0                                 7 P + 34 - 6 = 0                                                 7 P + 28 = 0                                                    7 P = - 28                                                 \[P=-\frac{28}{7}=-4\]


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