JEE Main & Advanced Physics Vectors Question Bank Fundamentals of Vectors

  • question_answer The angle between the two vectors \[\vec{A}=3\hat{i}+4\hat{j}+5\hat{k}\] and \[\vec{B}=3\hat{i}+4\hat{j}-5\hat{k}\] will be                                                         [Pb. CET 2001]

    A)            \[\text{9}0{}^\circ \]

    B)            \[0{}^\circ \]

    C) \[\text{6}0{}^\circ \]      

    D)            \[\text{45}{}^\circ \]

    Correct Answer: A

    Solution :

                 \[\cos \theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{|A||B|}=\frac{(3\hat{i}+4\hat{j}+5\hat{k})\,(3\hat{i}+4\hat{j}-5\hat{k})}{\sqrt{9+16+25}\sqrt{9+16+25}}\]                    \[=\frac{9+16-25}{50}=0\]                    Þ \[\cos \theta =0\], \[\therefore \] \[\theta =90{}^\circ \]    

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