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BCECE Engineering BCECE Engineering Solved Paper-2003

  • question_answer
    If angle between \[\vec{a}\]and\[\vec{b}\]is\[\frac{2\pi }{3}\] and if\[|\vec{a}|=5,|\vec{b}|=3,\]then\[|\vec{a}-\vec{b}|\]is equal to:

    A)  23                                         

    B)                   7                                            

    C)                   17                                         

    D)                   18

    Correct Answer: B

    Solution :

    Since,\[|\vec{a}|=5,|\vec{b}|=3\]and angle between \[\vec{a}\]and\[\vec{b}\]is \[\frac{2\pi }{3}.\] \[\therefore \] \[|\vec{a}-\vec{b}{{|}^{2}}=|\vec{a}{{|}^{2}}+|\vec{b}{{|}^{2}}-2|\vec{a}||\vec{b}|cos\frac{2\pi }{3}\]  \[={{5}^{2}}+{{3}^{2}}-2.5.3\left( -\frac{1}{2} \right)\] \[25+9+15\] \[=49\]                 \[\,\Rightarrow \]            \[|\vec{a}-\vec{b}|=7\]


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