Mathematics - Vector Question with Solution | TestHub

$(\vec{c}-\vec{a})\times (\vec{a}\times \vec{b})=0$, so $\vec{c}-\vec{a}=\lambda (\vec{a}\times \vec{b})$. Dotting with $\vec{a}\times \vec{b}$ gives $8=4\lambda$, hence $\lambda =2$. Therefore $|\vec{c}{|}^2=|\vec{a}{|}^2+4|\vec{a}\times \vec{b}{|}^2=9+16=25$.