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JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    If \[\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,,\overset{\to }{\mathop{c}}\,\] are unit vectors, then the value of \[|\overset{\to }{\mathop{a}}\,-2\overset{\to }{\mathop{b}}\,{{|}^{2}}+|\overset{\to }{\mathop{b}}\,-2\overset{\to }{\mathop{c}}\,{{|}^{2}}+|\overset{\to }{\mathop{c}}\,-2\overset{\to }{\mathop{a}}\,{{|}^{2}}\] does not exceed

    A)  12                                         

    B)  15

    C)  18                                         

    D)  21

    Correct Answer: D

    Solution :

    \[E=|\overrightarrow{a}-2\overrightarrow{b}{{|}^{2}}+|\overrightarrow{b}-2\overrightarrow{c}{{|}^{2}}+|\overrightarrow{c}-2\overrightarrow{a}{{|}^{2}}\] \[E=5\left( {{\overrightarrow{a}}^{2}}+{{\overrightarrow{b}}^{2}}+{{\overrightarrow{c}}^{2}} \right)-4\left( \overrightarrow{a}\cdot \overrightarrow{b}+\overrightarrow{b}\cdot \overrightarrow{c}+\overrightarrow{c}\cdot \overrightarrow{a} \right)\] \[E=15-4\left( \overrightarrow{a}\cdot \overrightarrow{b}+\overrightarrow{b}\cdot \overrightarrow{c}+\overrightarrow{c}\cdot \overrightarrow{a} \right)\le 15-4\left( \frac{-3}{2} \right)\] \[E\le 21\]


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