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JEE Main & Advanced Physics Vectors Question Bank Multiplication of Vectors

  • question_answer
    If a vector \[2\hat{i}+3\hat{j}+8\hat{k}\]is perpendicular to the vector \[4\hat{j}-4\hat{i}+\alpha \hat{k}\]. Then the value of \[\alpha \] is           [CBSE PMT 2005]

    A)                 ?1          

    B)                 \[\frac{1}{2}\]

    C)                 \[-\frac{1}{2}\] 

    D)                 1

    Correct Answer: C

    Solution :

                        Given vectors can be rewritten as \[\overrightarrow{A}=2\hat{i}+3\hat{j}+8\hat{k}\] and \[\overrightarrow{B}=-4\hat{i}+4\hat{j}+\alpha \hat{k}\] Dot product of these vectors should be equal to zero because they are perpendicular.                 \ \[\overrightarrow{A}\,.\,\overrightarrow{B}=-8+12+8\alpha =0\] Þ \[8\alpha =-4\] Þ \[\alpha =-1/2\]


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