JEE Main & Advanced Physics Vectors Question Bank Multiplication of Vectors

  • question_answer
    The position vectors of points A, B, C and D are \[A=3\hat{i}+4\hat{j}+5\hat{k},\,\,B=4\hat{i}+5\hat{j}+6\hat{k},\,\,C=7\hat{i}+9\hat{j}+3\hat{k}\] and \[D=4\hat{i}+6\hat{j}\] then the displacement vectors AB and CD are

    A)                 Perpendicular   

    B)                 Parallel

    C)                 Antiparallel        

    D)                 Inclined at an angle of \[\text{6}0{}^\circ \]

    Correct Answer: D

    Solution :

                        \[\overrightarrow{AB}=(4\hat{i}+5\hat{j}+6\hat{k})-(3\hat{i}+4\hat{j}+5\hat{k})\]=\[\hat{i}+\hat{j}+\hat{k}\]                 \[\overrightarrow{CD}=(4\hat{i}+6\hat{j})-(7\hat{i}+9\hat{j}+3\hat{k})\]             \[=-3\hat{i}-3\hat{j}-3\hat{k}\]                 \[\overrightarrow{AB}\] and \[\overrightarrow{CD}\] are parallel, because its cross-products is 0.


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