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

  • question_answer
    If ABCD is a parallelogram and the position vectors of A, B, C are \[\mathbf{i}+3\mathbf{j}+5\mathbf{k},\,\,\mathbf{i}+\mathbf{j}+\mathbf{k}\] and \[7\mathbf{i}+7\mathbf{j}+7\mathbf{k},\] then the position vector of D will be

    A) \[7\mathbf{i}+5\mathbf{j}+3\mathbf{k}\]      

    B) \[7\mathbf{i}+9\mathbf{j}+11\mathbf{k}\]

    C) \[9\mathbf{i}+11\mathbf{j}+13\mathbf{k}\] 

    D) \[8\mathbf{i}+8\mathbf{j}+8\mathbf{k}\]

    Correct Answer: B

    Solution :

    Let position vector of D is \[x\mathbf{i}+y\mathbf{j}+z\mathbf{k},\] then \[\overrightarrow{AB}=\overrightarrow{DC}\] \[\Rightarrow -2\mathbf{j}-4\mathbf{k}=(7-x)\mathbf{i}+(7-y)\mathbf{j}+(7-z)\mathbf{k}\]                                 \[\Rightarrow x=7,\,\,y=9,\,\,z=11.\] Hence position vector of \[D\] will be \[7\mathbf{i}+9\mathbf{j}+11\,\mathbf{k}\].


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