Among all the unit vectors in ,
find the one for which the sum is minimal.
Hint: , where .
Any help would be appreciated.
The dot product $\displaystyle \vec{u}\cdot\vec{v}$ will be minimal when $\displaystyle \vec{u}$ is pointing in the opposite direction to $\displaystyle \vec{v}$. That suggests taking $\displaystyle \vec{u} = \begin{bmatrix}-1\\-5\\-4\end{bmatrix}$. But that is not a unit vector. So you will need to divide that vector by its length.
Is that enough of a hint?