Looks to me like your answer is the same as the one in the book, with the exception that you have a term of $7\vec a \vec b$, by which I assume you mean $7|\vec a| \vec b|$, whereas the book's answer is $7 \vec a \cdot \vec b$. The reason the book has the dot product is that $\vec a$ and $\vec b$ are not necessarily orthogonal, the way perhaps other examples in your book may be.