Let $\vec a$ and $\vec b$ be non-collinear vectors in $\mathbb R^3$ and let $|\vec a|=|\vec b|=\sqrt2$. Calculate the angle between vectors $\vec a$ and $\vec b$ if the area of the parallelogram spanned by vectors $\vec a\times\vec b$ and $\vec a+\vec b$ is twice the area of the parallelogram spanned by vectors $\vec a$ and $\vec b$.
Can someone please help me solve this problem? I understand that $|(\vec a\times\vec b)\times(\vec a+\vec b)|=2|\vec a\times\vec b|.$ But I dont know how to compute it. Also vectors $\vec a$ and $\vec b$ be non-collinear vectors so $\vec a\cdot\vec b\neq 0$. And $\cos\langle\vec a,\vec b\rangle=\dfrac{\vec a\cdot\vec b}{|\vec a||\vec b|}$.