Mathematics - Vector Question with Solution | TestHub

As$\overrightarrow{u}=\lambda \left[\overrightarrow{a}\times (\overrightarrow{a}\times \overrightarrow{b})\right]$

$\overrightarrow{u}=\lambda \left[\left[\overrightarrow{a}.\overrightarrow{b}\right]\overrightarrow{a}-|\overrightarrow{a}{|}^2\overrightarrow{b}\right]$

$\overrightarrow{u}=\lambda \left[2\overrightarrow{a}-14\overrightarrow{b}\right]$

$\overrightarrow{u}.\overrightarrow{b}=2\lambda \left[\overrightarrow{a}.\overrightarrow{b}-7|\overrightarrow{b}{|}^2\right]$

$=2\lambda \left[2-14\right]$

$24=-24\lambda$

$\lambda =-1$

$\overrightarrow{u}=14\overrightarrow{b}-2\overrightarrow{a}$

$\overrightarrow{u}=-4\widehat{i}+8\widehat{j}+16\widehat{k}$

$|\overrightarrow{u}{|}^2=4^2+8^2+{16}^2$

$=336$