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RAJASTHAN PMT Rajasthan - PMT Solved Paper-1999

  • question_answer
    If \[\hat{n}=a\hat{i}+b\hat{j},\] is perpendicular to (\[\hat{i}+\hat{j},\]then value of \[a\] and b is:

    A)  1, 0                       

    B)         -2, 0

    C)  -3, 0                     

    D)         \[\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\]

    Correct Answer: D

    Solution :

                     \[\hat{A}.\hat{B}=O\,\,\,\,\,\,\,\,\,\,\,\,(\vec{A}\bot \vec{B})\] \[\begin{align}   & (a\hat{i}+b\hat{j}).(\hat{i}+\hat{j}) \\  & a+b=0 \\ \end{align}\] \[\therefore \]\[a=\frac{1}{\sqrt{2}'}b=-\frac{1}{\sqrt{2}}\]


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