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JEE Main & Advanced Mathematics Vector Algebra Question Bank Self Evaluation Test - Vector Algebra

  • question_answer
    If \[\vec{a}=2\hat{i}+2\hat{j}+3\hat{k},\vec{b}=-\hat{i}+2\hat{j}+\hat{k}\] and \[\overrightarrow{c}=3\hat{i}+\hat{j}\]are three vectors such that \[\vec{a}+t\vec{b}\] is perpendicular to \[\vec{c}\], then what is t equal to?

    A) 8

    B) 6

    C) 4

    D) 2

    Correct Answer: A

    Solution :

    [a] \[\vec{a}+t\vec{b}=(2-t)\hat{i}+(2+2t)\hat{j}+(3+t)\hat{k}\] \[(\vec{a}+t\vec{b})\] and \[\vec{c}\] is perpendicular. Therefore, \[(\vec{a}+t\vec{b}).\vec{c}=0\] \[3(2-t)+2+2t=0\] \[6-3t+2t+2=0\] \[t=8\]


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