Assuming that $k$ may range over $\mathbb R$, and let $v_k=(k,k,3-k)$, start out by considering the function $f(k)=\|v_k\|$. What you want is to locate the minimum of $f$. Now, work with the definition of the length of a vector. You will see that it contains a square root. Make your life a lot easier by noticing that it is actually the same problem to find the minimum of the function $g(k)=\|v_k\|^2$, so now the square root is gone. Now you just have a rather simple single variable real valued function. Find its minimum using standard calculus techniques.