Word vectors can be applied to word analogy tasks. A word analogy completion task is defined by the relationship $a:b::c:d$, meaning "$a$ is to $b$ as $c$ is to $d$". Given the first three words $a$, $b$, and $c$, the objective is to find the missing word $d$. If we denote the numerical representation of a word $w$ as $\textrm{vec}(w)$, we can complete the analogy by evaluating the vector arithmetic $\textrm{vec}(c) + \textrm{vec}(b) - \textrm{vec}(a)$ and finding the word in the vocabulary whose vector is most similar to this result.