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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

  • question_answer
    The two variable vectors\[3x\hat{i}+y\hat{j}-3\hat{k}\]and\[x\hat{i}-4y\hat{j}+4\hat{k}\]are orthogonal to each other, then the locus of\[(x,\text{ }y)\]is

    A)  hyperbola         

    B)  circle

    C)  straight line       

    D)         ellipse

    E)  parabola

    Correct Answer: A

    Solution :

    Given vectors are orthogonal. \[\therefore \]\[(3x\hat{i}+y\hat{j}-3\hat{k}).(x\hat{i}-4y\hat{i}+4\hat{k})=0\] \[\Rightarrow \]               \[3{{x}^{2}}-4{{y}^{2}}-12=0\] \[\Rightarrow \]               \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{3}=1\] Hence, it represents a hyperbola.


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