Not to confuse you, to get you used to both kinds of notation. The length of v is sometimes called the magnitude or the norm of v . One last thing. It's always hard to discuss addition of vectors. But that is a definition that is easier to visualize than compute with.
Scalar multiplication is easier.
The best way to deal with vectors analytically is to break them into components, which means to express them in terms of standard vectors. Then, any vector v can be compared to these, by seeing how much of v is in the direction of i , then how much is in the direction of j , and finally k . The text has two notations for a vector v in terms of these components. The second notation is much more standard, and we will be using it almost exclusively. In terms of these components, it's easy to compute vector addition.