I have a homework question that asking to
Find all scalars $k$ such that $\|kv\| = 10$ when $v=(1,-4,6)$.
What I did that that I found the norm of $v$ which I found to be $\sqrt{53}$. Then I took that answer and multiplied by $k$ to get $10$ like this: $\sqrt{53}\cdot k=10$, $ k=\frac{10}{\sqrt{53}} $ I don't think this approach is right because it doesn't deal with the $k$ being calculated within the norm. I just don't know how to do it that was so any pointers would be greatly appreciated.