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

  • question_answer
    If the points \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\mathbf{a}+k\,\mathbf{b}\] be collinear, then k =

    A) 0             

    B) 2

    C) 2             

    D) Any real number

    Correct Answer: D

    Solution :

    \[(\mathbf{a}-\mathbf{b})-(\mathbf{a}+\mathbf{b})=\left[ (\mathbf{a}+k\mathbf{b})-(\mathbf{a}-\mathbf{b}) \right]\]                 \[\Rightarrow -2\mathbf{b}=(k+1)\mathbf{b}\]. Hence \[k\in R.\]


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