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

  • question_answer
    Three points whose position vectors are \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\mathbf{a}+k\mathbf{b}\] will be collinear, if the value of k is                  [IIT 1984]

    A) Zero       

    B) Only negative real number

    C) Only positive real number

    D) Every real number

    Correct Answer: D

    Solution :

    \[\overrightarrow{AB}=\lambda \overrightarrow{BC}\],                (for collinearity) Here \[\overrightarrow{AB}=-2\mathbf{b},\] \[\overrightarrow{BC}=(k+1)\mathbf{b}\] Hence \[\forall \,\,k\in R\Rightarrow \overrightarrow{AB}=\lambda \overrightarrow{BC}.\]


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