If | A + B |=| A |+| B | the angle between

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.