It is known that $\vec{u} [3,4]$ and $\vec{v}[2,k]$. And I need to find k such that the norm of the projection of ⃗ over ⃗ equals to 1.
I am trying to obtain the norm of the vector $\frac{6+4k}{25} \vec{u}$.
However, the answer key tells me that the norm would be $\frac{|6+4k|}{5}$
But I am not sure what to do in order to obtain such an answer?
$$\Big\| \frac{6+4k}{25} u\Big\| = \frac{|6+4k|}{25}\|u\| = \frac{|6+4k|}{25}\sqrt{3^2+4^2} = \frac{|6+4k|}{5}$$