Answer
36.6
Work Step by Step
$|\vec{a}\times(\vec{b}\times\vec{a})|=a\,|\vec{b}\times\vec{a}|\sin\theta$ where $\theta$ is the angle between $\vec{a}$ and $(\vec{b}\times\vec{a})$.
As $\vec{b}\times\vec{a}$ is a vector perpendicular to both $\vec{b}$ and $\vec{a}$, we have
$|\vec{a}\times(\vec{b}\times\vec{a})|=a\,|\vec{b}\times\vec{a}|\times\sin 90^{\circ}=a\,|\vec{b}\times\vec{a}|$
$=a(ba\sin\beta)$ where $\beta$ is the angle between $\vec{b}$ and $\vec{a}$.
Given: a=3.90, b=2.70 and $\beta=63.0^{\circ}$.
Therefore,
$|\vec{a}\times(\vec{b}\times\vec{a})|=3.90(2.70\times3.90\times\sin63^{\circ})=36.6$
