Let $\vec a$, $\vec b$, $\vec c$ and $\vec y$ be the three dimensional vectors $$\vec a = 2\,\mathit{\vec j}+3\,\mathit{\vec k},\quad \vec b = -3\,\mathit{\vec i}+7\,\mathit{\vec j}+8\,\mathit{\vec k},\quad \vec c = 3\,\mathit{\vec i}-5\,\mathit{\vec j},\quad \vec y = 4\,\mathit{\vec i}-\,\mathit{\vec j}$$

Perform the following operations on these vectors:

(a) $\vec c\cdot\vec a + \vec a\cdot\vec y =$

(b) $(\vec a\cdot\vec b)\,\vec a =$

(c) $( (\vec c\cdot\vec c)\,\vec a )\cdot\vec a =$