Calculate forward direction vector using 2 vectors

Question

I have 2 vectors:

a(1,2,5) and b(-5,8,1)

I need to calculate the forward direction vector from vector A to vector B.

How do I do this? Is there a formula?

Answer 1

The direction vector from vector a to vector b can be calculated as followed:

$$\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$$

In this case:

$\overrightarrow{AB}=\begin{pmatrix}-5\\8\\1\end{pmatrix}-\begin{pmatrix}1\\2\\5\end{pmatrix}=\begin{pmatrix}-6\\6\\-4\end{pmatrix}$

So the direction vector from $a$ to $b$ is $\overrightarrow{AB}=\begin{pmatrix}-6\\6\\-4\end{pmatrix}$.