CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    Let\[\overrightarrow{a}\]and\[\overrightarrow{b}\]be two unit vectors such that angle between them is\[60{}^\circ \]. Then\[|\overrightarrow{a}-\overrightarrow{b}|\]is equal to:

    A)  \[\sqrt{5}\]                                       

    B)  \[\sqrt{3}\]

    C)  \[0\]                                    

    D)  \[1\]

    E)  \[\sqrt{2}\]

    Correct Answer: D

    Solution :

    \[|\overrightarrow{a}-\overrightarrow{b}{{|}^{2}}=|\overrightarrow{a}{{|}^{2}}+|\overrightarrow{b}{{|}^{2}}-2|\overrightarrow{a}||\overrightarrow{b}|\cos \theta \] \[\Rightarrow \]\[|\overrightarrow{a}-\overrightarrow{b}{{|}^{2}}=1+1-2\cos 60{}^\circ \] \[=2-1\] \[\Rightarrow \]               \[|\overrightarrow{a}-\overrightarrow{b}|=1\]


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