# Help for understanding a vectorial equation found in a paper.

Trying to implement a code for the algorithm described in this paper I found something not very clear to me that leads me to misunderstand the whole concept.

To calculate the vector $\vec{b_{3d}}$ the paper (page 3) suggests to use the following equation:

To me it look like a normal vectorial equation where you divide one vector by its normalized value. Something very trivial.

But I was wondering that the variables $e_{x}, e_{v}$ are previously defined as a vector of the error of the variables $x, v$ as: $e_{x} = x-x_{d} \quad e_{v} = v-v_{d}$ at the beginning of the paper where $x,v$ are vectors: $x \in \mathbb{R}^{3}$ and $v \in \mathbb{R}^{3}$

So now I have the following questions:

1. I suppose that the equation above is not useful to get $\vec{b_{3d}}$ if I treat $x,v$ as vectors. But in this case I cannot do nothing since in the paper doesn't explain which vector element should I consider to calculate $\vec{b_{3d}}$;
2. In the equation compares the term $e_{3}$ which is the unity vector of the $Z$ axis. Maybe the authors wanted to point out that you should consider the gravity along Z, but why should I put a unity vector in an equation, if it is suppose to have all term as scalar?;

Anyway... good day.

• I don't know about anyone else, but your picture of the equation isn't displaying on my page and I've tried refreshing a couple of times. Commented Dec 28, 2014 at 9:31
• Look at equation nr. 12 on this paper
– Dave
Commented Dec 28, 2014 at 9:41