The given vectors are $\vec a$=$\vec i$ + $\vec j$ − $\vec k$ , $\vec b$=−2$\vec i$−$\vec j$+2$\vec k$ $\vec c$ =$\vec i$−$\vec j$ + 2$\vec k$. a.) Decompose vector $\vec c$ into components by vectors $\vec a$, $\vec b$ and $\vec a$×$\vec b$. b.) Calculate the angle formed by vector $\vec c$ with the plane defined by vectors $\vec a$ and $\vec b$.
I dont know where to start, I think for task a.) vector c should be:
$\vec{c} = \alpha\vec{a}+\beta\vec{b}+\gamma(\vec{a}x\vec{b}) $
I would appreciate any help in solving this problem.