Find the angle between the two vectors: $\overrightarrow{a}=3\hat{\mathrm{i}}+2\hat{\mathrm{j}}+5\hat{\mathrm{k}}$, $\overrightarrow{b}=5\hat{\mathrm{i}}+3\hat{\mathrm{j}}+\hat{\mathrm{k}}$.

Use the concept of dot product and mod of a vector, from which we can find the angle between two vectors, so the angle between the two vectors can find by the formula of, 
$$\begin{gathered} \cos \theta =\frac{\overrightarrow{A}·\overrightarrow{B}}{\left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|}=\frac{\left(3\hat{i}+2\hat{j}+5\hat{k}\right)·\left(5\hat{i}+3\hat{j}+\hat{k}\right)}{\left|3\hat{i}+2\hat{j}+5\hat{k}\right|\left|5\hat{i}+3\hat{j}+\hat{k}\right|} \\ \Rightarrow \cos \theta =\frac{15+6+5}{\sqrt{3^2+2^2+5^2}\sqrt{5^2+3^2+1^2}} \\ \Rightarrow \cos \theta =\frac{26}{\sqrt{1330}} \end{gathered}$$