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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 41

  • question_answer
    If \[\vec{a}=(1,-1,2),\] \[\vec{b}=(-2,3,5),\]\[\vec{c}=(2,-2,4),\]and \[\hat{i}\] is the unit vector in the x-direction, then \[(\vec{a}-2\vec{b}+3\vec{c})\hat{i}=\]

    A) 11        

    B)        15     

    C) 18        

    D)        36

    Correct Answer: A

    Solution :

    \[\vec{a}=(1,-1,2),\vec{b}=(-2,3,5),\vec{c}=(2,-2,4)\] So, \[\vec{a}=(1,-1,2)\equiv \hat{i}-\hat{j}+2\hat{k};\hat{b}\] \[=(-2,3,5)\equiv -2\hat{i}+3\hat{j}+5\hat{k}\] and \[=(2,-2,4)\equiv 2\hat{i}-2\hat{j}+4\hat{k}\] \[\Rightarrow \,\vec{a}-2\vec{b}+3\vec{c}=(\hat{i}-\hat{j}+2\hat{k})-2(-2\hat{k}+3\hat{j}+5\hat{k})\]                                     \[+3(2\hat{i}-2\hat{j}+4\hat{k})\] \[=11\hat{i}-13\hat{j}+4\hat{k}\] and \[(\vec{a}-2\vec{b}+3c).\hat{i}=11.\]


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