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JEE Main & Advanced JEE Main Online Paper (Held On 08 April 2018)

  • question_answer
    Let \[\overset{\to }{\mathop{u}}\,\] be a vector coplanar with the vectors \[\overset{\to }{\mathop{a}}\,=2\widehat{i}+3\widehat{j}-\widehat{k}\] and \[\overset{\to }{\mathop{b}}\,=\widehat{j}+\widehat{k}.\] If \[\overset{\to }{\mathop{u}}\,\] is perpendicular to \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{u}}\,\cdot \overset{\to }{\mathop{b}}\,=24\], then \[{{\left| \overset{\to }{\mathop{u}}\, \right|}^{2}}\] is equal to:   [JEE Main Online 08-04-2018]

    A)  256                            

    B)  84

    C)  336                            

    D)  315

    Correct Answer: C

    Solution :

    \[\overset{\to }{\mathop{\text{u}}}\,=\lambda \overset{\to }{\mathop{a}}\,\times \left( \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right)\] \[=\lambda \left[ \left( \overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{b}}\, \right)\overset{\to }{\mathop{a}}\,-(\overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{a}}\,)\overset{\to }{\mathop{b}}\, \right]\] \[=\lambda \left[ 2\overset{\to }{\mathop{a}}\,-14\overset{\to }{\mathop{b}}\, \right]\] \[=2\lambda \left[ \overset{\to }{\mathop{a}}\,-7\overset{\to }{\mathop{b}}\, \right]=2\lambda \left( 2\text{\hat{i}-4}\widehat{\text{j}}-8\widehat{\text{k}} \right)\] \[\overset{\to }{\mathop{\text{u}}}\,.\overset{\to }{\mathop{\text{b}}}\,=24\] \[-12\times 2\lambda =24\] \[\lambda =-1\] \[\overset{\to }{\mathop{\text{u}}}\,=-4\widehat{\text{i}}+8\widehat{\text{j}}+16\widehat{\text{k}}\] \[{{\left| \overset{\to }{\mathop{\text{u}}}\, \right|}^{2}}=16+64+256\] \[{{\left| \overset{\to }{\mathop{\text{u}}}\, \right|}^{2}}=336\]


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