a
For two vectors \(A \square A \rightarrow\) and \(B \square B \rightarrow\), the angle between them being \(\theta \theta\), the magnitude of the resultant vector \(A + B \rightarrow A + B \rightarrow\) is given by,

\(| A + B |=\sqrt{| A |^2+| B |^2+2 AB \cos \theta}\)

Now in the problem we've,

\(| A + B |=| A |+| B |\)

Squaring on both sides,

\(\begin{array}{l}| A + B |^2=(| A |+| B |)^2 \\| A |^2+| B |^2+2| A || B | \cos \theta=| A |^2+| B |^2+2| A || B | \\\Rightarrow \cos \theta=1\end{array}\)

assuming neither of the vectors are \(zero\) vectors.