A) 256
B) 84
C) 336
D) 315
Correct Answer: C
Solution :
\[\overset{\to }{\mathop{\text{u}}}\,=\lambda \overset{\to }{\mathop{a}}\,\times \left( \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right)\] \[=\lambda \left[ \left( \overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{b}}\, \right)\overset{\to }{\mathop{a}}\,-(\overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{a}}\,)\overset{\to }{\mathop{b}}\, \right]\] \[=\lambda \left[ 2\overset{\to }{\mathop{a}}\,-14\overset{\to }{\mathop{b}}\, \right]\] \[=2\lambda \left[ \overset{\to }{\mathop{a}}\,-7\overset{\to }{\mathop{b}}\, \right]=2\lambda \left( 2\text{\hat{i}-4}\widehat{\text{j}}-8\widehat{\text{k}} \right)\] \[\overset{\to }{\mathop{\text{u}}}\,.\overset{\to }{\mathop{\text{b}}}\,=24\] \[-12\times 2\lambda =24\] \[\lambda =-1\] \[\overset{\to }{\mathop{\text{u}}}\,=-4\widehat{\text{i}}+8\widehat{\text{j}}+16\widehat{\text{k}}\] \[{{\left| \overset{\to }{\mathop{\text{u}}}\, \right|}^{2}}=16+64+256\] \[{{\left| \overset{\to }{\mathop{\text{u}}}\, \right|}^{2}}=336\]You need to login to perform this action.
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