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JEE Main & Advanced Mathematics Vector Algebra Question Bank Critical Thinking

  • question_answer
    If \[\overrightarrow{A}=\mathbf{i}+2\mathbf{j}+3\mathbf{k},\,\,\,\overrightarrow{B}=-\mathbf{i}+2\mathbf{j}+\mathbf{k}\] and \[\overrightarrow{C}=3\mathbf{i}+\mathbf{j},\] then the value of t such that \[\overrightarrow{A}+t\overrightarrow{B}\] is at right angle to vector \[3\mathbf{i}+4\mathbf{j}\] is       [RPET 2002]

    A) 2

    B) 4

    C) 5

    D) 6

    Correct Answer: C

    Solution :

    • \[\overrightarrow{A}+t\,\overrightarrow{B}=(\mathbf{i}+2\mathbf{j}+3\mathbf{k})+t(-\mathbf{i}+2\mathbf{j}+\mathbf{k})\]                              
    • \[=\mathbf{i}(1-t)+\mathbf{j}(2+2t)+\mathbf{k}(3+t)\]                   
    • But it is perpendicular to \[\overrightarrow{C}=3\mathbf{i}+\mathbf{j},\]                   
    • So, \[\overrightarrow{C}\,\,.\,(\overrightarrow{A}+t\,\overrightarrow{B})=0\Rightarrow 3(1-t)+2+2t=0\Rightarrow t=5.\]


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