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NEET Sample Paper NEET Sample Test Paper-42

  • question_answer
    If \[\vec{A} = \vec{i} A cos\theta +\vec{j} A sin\theta ,\]then another vector \[\vec{B}\]which is orthogonal to \[\vec{A}\]can be expressed as:

    A) \[\vec{i}\,B cos\theta -\vec{j}\,B\,sin\theta \]        

    B) \[\vec{i}\,B sin\theta +\vec{j}\,B cos\theta \]

    C) \[\vec{i}\,B cos\theta +6\vec{j}\,B\,sin\theta \]

    D) \[\vec{i}\,B sin\theta +\vec{j}\,B cos\theta \]

    Correct Answer: B

    Solution :

    Two vectors are said to be orthogonal when their dot product is zero. \[\operatorname{A} = \hat{i} A Cos\theta  +\hat{j} A Sin\theta \][use option to reduce time] From option \[\left( b \right) \hat{i} B Sin\theta  - \hat{j} B Cos\theta .\] Dot product is zero \[\vec{A}. \left( {\vec{b}} \right)=AB Sin\theta  Cos\theta - AB Sin\theta  Cos\theta  =0\]


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