The angle between x axis and the vector i+j+k, is :

let $\vec{v}=\hat{i}$ be a vector along x axis

given vector $\vec{p}=\hat{i}+\hat{j}+\hat{k}$

$\vec{v} . \vec{p}=|\vec{v}||\vec{p}| \cos \theta$

$\theta$ → angle b/w $\vec{v}$ and $\vec{p}$

$\Rightarrow (\hat{i}) (\hat{i}+\hat{j}+\hat{k})=|\hat{i}||\hat{i}+\hat{j}+\hat{k}| \cos \theta$

$= 1 =1 \times \sqrt{3} \cos \theta$

$\cos \theta =\frac{1}{\sqrt{3}}$

$ \theta =\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$