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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, C are collinear, whose position vectors are \[\mathbf{i}-2\mathbf{j}-8\mathbf{k},\,\,5\mathbf{i}-2\mathbf{k}\] and \[11\,\mathbf{i}+\,3\,\mathbf{j}+7\mathbf{k}\] respectively, then the ratio in which B divides AC is                                                                      [RPET 1999]

    A) 1 : 2       

    B) 2 : 3

    C) 2 : 1       

    D) 1 : 1

    Correct Answer: B

    Solution :

    Let the B divide AC in ratio \[\lambda :1\], then                 \[5\mathbf{i}-2\mathbf{k}=\frac{\lambda (11\mathbf{i}+3\mathbf{j}+7\mathbf{k})+\mathbf{i}-2\mathbf{j}-8\mathbf{k}}{\lambda +1}\] \[\Rightarrow 3\lambda -2=0\] \[\Rightarrow \lambda =\frac{2}{3}\] i.e., ratio = 2 : 3.


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