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BCECE Engineering BCECE Engineering Solved Paper-2013

  • question_answer
    Let \[u=i+j,v=i-j\]and \[w=i+2j+3k\]. If \[\hat{n}\] is a unit vector such that \[u.\hat{n}=0\]and \[u.\hat{n}=0,\]then \[|w.\hat{n}|\]is equal to

    A)  3                            

    B)  0                            

    C)  1                     

    D)  2

    Correct Answer: A

    Solution :

    We have, \[u.\,\hat{n}=0\]and \[v.\,\hat{n}=0\] \[\Rightarrow \]\[\hat{n}\bot u\]and \[\hat{n}\bot v\] \[\Rightarrow \]\[\hat{n}=\pm \frac{u\times v}{|u\times v|}\] Now, \[u\times v=(i+j)\times (j-k)=-2k\] \[\therefore \]  \[\hat{n}=\pm k\] Hence, \[|\bar{w}.\hat{n}|=|(i+2j+3k).(\pm \,3k)|=3\]


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