# Math Help - Finding a unit vector

1. ## Finding a unit vector

Among all the unit vectors in ,
find the one for which the sum is minimal.
Hint: , where .
Any help would be appreciated.

2. Originally Posted by Shapeshift
Among all the unit vectors $\vec{u} = \begin{bmatrix}x\\y\\z\end{bmatrix}$ in ,
find the one for which the sum is minimal.
Hint: , where $\vec{v} = \begin{bmatrix}1\\5\\4\end{bmatrix}$.
The dot product $\vec{u}\cdot\vec{v}$ will be minimal when $\vec{u}$ is pointing in the opposite direction to $\vec{v}$. That suggests taking $\vec{u} = \begin{bmatrix}-1\\-5\\-4\end{bmatrix}$. But that is not a unit vector. So you will need to divide that vector by its length.

Is that enough of a hint?