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JEE Main & Advanced Mathematics Straight Line Question Bank Distance between two lines, Perpendicular distance of the line from a point Position of point w.r.t. line

  • question_answer
    \[(\sin \theta ,\cos \theta )\] and \[(3,\,2)\] lies on the same side of the line \[x+y=1\],  then \[\theta \] lies between                                [DCE 2005]

    A)            \[(0,\,\,\pi /2)\]                        

    B)            \[(0,\,\pi )\]

    C)            \[(\pi /4,\pi /2)\]                      

    D)            \[(0,\,\,\pi /4)\]

    Correct Answer: D

    Solution :

               As \[(\sin \theta ,\cos \theta )\]and (3, 2) lie on the same side of \[x+y-1=0\], they should be of same sign.                    \ \[\sin \theta +\cos \theta -1>\]as \[3+2-1>0\]                    Þ \[\sqrt{2}\sin \left( \theta +\frac{\pi }{4} \right)>1\]                    Þ \[\sin \left( \theta +\frac{\pi }{4} \right)>\frac{1}{\sqrt{2}}\Rightarrow 0<\theta <\frac{\pi }{4}\].


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