I partially understand the method but not fully so can someone please briefly go through the method. Help would be appreciated.

_______________________________________________

Q: The positions vectors with respect to the origin $\displaystyle O$ are:

$\displaystyle B: -4 \bold i + 4 \bold j - \bold k$,

$\displaystyle C: 5 \bold i - 2 \bold j + 11 \bold k$.

Find a vector equation for the line $\displaystyle BC$.

_______________________________________________

The Correct Answer:

$\displaystyle \bold r = \begin{pmatrix} -4 \\ 4 \\ -1 \end{pmatrix} + \mu \begin{pmatrix} 3 \\ -2 \\ 4 \end{pmatrix} $.