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JEE Main & Advanced AIEEE Solved Paper-2012

  • question_answer
    Let \[\hat{a}\] and \[\hat{b}\] be two unit vectors. If the vectors \[\vec{c}=\hat{a}+2\hat{b}\] and \[\vec{d}=5\hat{a}-4\hat{b}\] are perpendicular to each other, then the angle between \[\hat{a}\] and \[\hat{b}\] is:   AIEEE  Solved  Paper-2012

    A) \[\frac{\pi }{6}\]                                  

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

    C) \[\frac{\pi }{3}\]                                  

    D) \[\frac{\pi }{4}\]

    Correct Answer: C

    Solution :

                 \[\vec{c}=\hat{a}+2\hat{b}\] \[\vec{d}=5\hat{a}-4\hat{b}\] \[\vec{c}.\,\vec{d}=0\] \[\Rightarrow \,\,(\hat{a}+2\hat{b}).(5\hat{a}-4\hat{b})=0\]          \[\Rightarrow 5+6\hat{a}.\,\hat{b}-8=0\] \[\Rightarrow \hat{a}.\,\hat{b}=\frac{1}{2}\]                         \[\Rightarrow \theta =\frac{\pi }{3}\]


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