I have a question here that I don't know how to proceed:
$\vec{u} [3,4]$ and $\vec{v}[2,k]$ are two vectors where k belongs to real number. Find k such that the norm of the projection of $\vec{v}$ over $\vec{u}$ equals to 1.
What I am able to do is to find the equation for the projection $\vec{v}_\vec{u}$
- $\frac{\vec{u}\vec{v}}{\vec{u}\vec{u}}\vec{u}$
- $\frac{6+4k}{25} (3,4)$
However, I am not sure what should I do next to find the k such that the norm of the projection is 1 ?
Continuing your work, what's the norm of $\lambda\vec{u}$ where $\lambda\in \mathbb{R}$? What about the norm of $\frac{6+4k}{25}\vec{u}$?