If $\overrightarrow a=\hat i+\hat j+p\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j+\hat k$, then $|\overrightarrow a+\overrightarrow b|=|\overrightarrow a|+|\overrightarrow b|$ holds for ?

Question

$\begin{array}{1 1} All \;real\;p \\ No\;real\;p \\ p=1 \\ p=-1 \end{array} $