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KVPY Sample Paper KVPY Stream-SX Model Paper-6

  • question_answer
    The vector \[\vec{c}\] is perpendicular to the vectors \[\vec{a}=(2,\,\,-3,\,\,1),\,\,\vec{b}=(1,\,\,-2,\,\,3)\] and satisfies the condition \[\vec{c}.\,\,(\hat{i}+2\hat{j}+7\hat{k})=10.\] Then the vector \[\vec{c}=\]

    A) (7, 5, 1)            

    B) \[(-7,\,\,-5,\,\,-1)\]

    C) \[(1,\,\,1,\,\,-1)\] 

    D)        none of these

    Correct Answer: A

    Solution :

    Let \[\vec{c}=\lambda \,(\vec{a}\times \vec{b})\]
    Hence \[\lambda \,(\vec{a}\times \vec{b})\cdot (\hat{i}+2\hat{j}-7\hat{k})=10\]
    But \[\vec{a}\times \vec{b}=(-7\hat{i}-5\hat{j}-\hat{k}),\]
    let         \[\vec{c}=\lambda \,(7\hat{i}+5\hat{j}+\hat{k})\]
    \[\Rightarrow \] \[\vec{c}=-\,(\vec{a}\times \vec{b})\]


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