For vector v=<3,2,-4>, how do you find the length and the unit vector in the same direction?
All you gotta do is divide the vector by its length.
$\displaystyle |\vec{v}|=(\vec{v} \cdot \vec{v})^{1/2}$
So for any vector $\displaystyle \vec{v}$, you know that $\displaystyle \frac{\vec{v}}{|\vec{v}|}$ is a vector of unit length in the same direction as $\displaystyle \vec{v}$ you just multiplied it by a scalar to adjust its length to be 1.