If $\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{b}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$, then find the angle between the vectors $2 \mathbf{a}+\mathbf{b}$ and $\mathbf{a}+2 \mathbf{b}$.

Question

If $\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{b}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$, then find the angle between the vectors $2 \mathbf{a}+\mathbf{b}$ and $\mathbf{a}+2 \mathbf{b}$., $\cos ^{-1}\left(\frac{36}{\sqrt{42 \times 35}}\right)$, $\cos ^{-1}\left(\frac{72}{\sqrt{24 \times 32}}\right)$, $\cos ^{-1}\left(\frac{52}{\sqrt{74 \times 65}}\right)$, $\cos ^{-1}\left(\frac{24}{\sqrt{18 \times 32}}\right)$

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