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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2006

  • question_answer
    If \[\overrightarrow{A}=\hat{i}+2\hat{j}+3\hat{k},\overrightarrow{B}=-\hat{i}+2\hat{j}+\hat{k}\]and \[\overrightarrow{C}=3\hat{i}+\hat{j},\]then\[\overrightarrow{A}+t\overrightarrow{B}\] is perpendicular to \[\overrightarrow{C},\] if t is equal to:

    A)  \[-5\]                   

    B)         4

    C)  5                            

    D)         \[-4\]

    E)  \[-7\]

    Correct Answer: C

    Solution :

    Now, \[\overrightarrow{A}+t\overrightarrow{B}=(1-t)\hat{i}+(2+2t)\hat{j}+(3+t)\hat{k}\] \[(\overrightarrow{A}+t\overrightarrow{B}).\overrightarrow{C}=3(1-t)+2+2t=0\] \[\Rightarrow \]\[-3t+2t+3+2=0\] \[\Rightarrow \]\[-t=-5\]\[\Rightarrow \]\[t=5\]


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