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JEE Main & Advanced Sample Paper JEE Main Sample Paper-17

  • question_answer
    Let \[\hat{a}\] and \[\hat{c}\] be unit vectors at an angle \[\frac{\pi }{3}\] with each other. If \[\left( \hat{a}\times (\hat{b}\,\times \hat{c}) \right).(\hat{a}\times \hat{c})=5\] then the value of \[[\hat{a}\hat{b}\hat{c}]\] is

    A)  0                            

    B)  5

    C) \[~-10\]                               

    D)  20

    Correct Answer: C

    Solution :

     \[(\hat{a}\times (\vec{b}\times \vec{c})).(\hat{a}\times \hat{c})=(\hat{a}.\hat{c})[\vec{b}\hat{a}\hat{c}]=5\] \[\Rightarrow \]\[[\hat{b}\hat{a}\hat{c}]=10\] \[\Rightarrow \]\[[\hat{a}\hat{b}\hat{c}]=-10\]


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