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

  • question_answer
    If the position vectors of the points A, B, C be \[\mathbf{a},\ \mathbf{b}\], \[3\mathbf{a}-2\mathbf{b}\] respectively, then the points A, B, C are                                                                                     [MP PET 1989]

    A) Collinear

    B) Non-collinear

    C) Form a right angled triangle

    D) None of these

    Correct Answer: A

    Solution :

    Here \[\overrightarrow{AB}=\mathbf{b}-\mathbf{a}\] and \[\overrightarrow{AC}=(3\mathbf{a}-2\mathbf{b})-(\mathbf{a})=-2(\mathbf{b}-\mathbf{a})\] Therefore, it is of the form \[\overrightarrow{AB}=m\overrightarrow{AC}.\] Hence  A, B, C are collinear.        


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