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Manipal Engineering Manipal Engineering Solved Paper-2010

  • question_answer
    If\[P(\overrightarrow{\mathbf{p}}),\text{ }Q(\overrightarrow{\mathbf{q}}),\text{ }R(\overrightarrow{\mathbf{r}})\]and\[S(\overrightarrow{\mathbf{s}})\]be four points such that\[3\overrightarrow{\mathbf{p}}+8\overrightarrow{\mathbf{q}}=6\overrightarrow{\mathbf{r}}+5\overrightarrow{\mathbf{s}}\], then the lines\[PQ\] and\[RS\]are

    A)  skew                                   

    B)  intersecting

    C)  parallel               

    D)         None of these

    Correct Answer: B

    Solution :

    Given,\[3\overrightarrow{\mathbf{p}}+8\overrightarrow{\mathbf{q}}=6\overrightarrow{\mathbf{r}}+5\overrightarrow{\mathbf{s}}\] \[\Rightarrow \]\[\frac{3\overrightarrow{\mathbf{p}}+8\overrightarrow{\mathbf{q}}}{8+3}=\frac{6\overrightarrow{\mathbf{r}}+5\overrightarrow{\mathbf{s}}}{6+5}\] \[\Rightarrow \]The point which divides PQ in ratio\[8:3\]in the same as the point which divides\[RS\]in the ratio\[5:6\]. Hence, the line\[PQ\]and\[RS\]intersect.


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