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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    If three points A, B and C have position vectors \[(1,\,x,\,3),\,\,(3,\,4,\,7)\] and \[ap+bq+cr=1\] respectively and if they are collinear, then \[(x,\,y)=\]                                                                                              [EAMCET 2002]

    A) (2, ? 3)

    B) (? 2, 3)

    C) (2, 3)      

    D) (? 2, ? 3)

    Correct Answer: A

    Solution :

    If A, B, C are collinear. Then \[\overrightarrow{AB}=\lambda \,\overrightarrow{BC}\] Þ  \[2\mathbf{i}+(4-x)\mathbf{j}+4\mathbf{k}=\lambda \,[(y-3)\mathbf{i}-6\mathbf{j}-12\mathbf{k}]\] \[\Rightarrow \,\,\,2=(y-3)\lambda \]                                     .....(i)  and \[4-x=-6\,\lambda \]                              .....(ii) Þ  \[4=-12\,\lambda \,\,\,\,\,\Rightarrow \,\,\lambda =\frac{-1}{3}\] By (i), \[y=-3\] and by (ii), \[x=2\]; \[\therefore \,\,\,(x,\,y)=(2,\,-3).\]  


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