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(B) The centroid of a triangle with vertices having position vectors $\vec{a}, \vec{b},$ and $\vec{c}$ is given by the formula: $	ext{Centroid} = \fr

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$\frac{4i + 4j + k}{3}$

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(B) The centroid of a triangle with vertices having position vectors $\vec{a}, \vec{b},$ and $\vec{c}$ is given by the formula: $	ext{Centroid} = \frac{\vec{a} + \vec{b} + \vec{c}}{3}$.Given vertices are $\vec{a} = \hat{i} + 2\hat{j}$,$\vec{b} = 2\hat{i} + \hat{j}$,and $\vec{c} = \hat{i} + \hat{j} + \hat{k}$.Substituting these values into the formula:$	ext{Centroid} = \frac{(\hat{i} + 2\hat{j}) + (2\hat{i} + \hat{j}) + (\hat{i} + \hat{j} + \hat{k})}{3}$$= \frac{(1+2+1)\hat{i} + (2+1+1)\hat{j} + (0+0+1)\hat{k}}{3}$$= \frac{4\hat{i} + 4\hat{j} + \hat{k}}{3}$.

Find the centroid of the triangle whose vertices are $i + 2j, 2i + j, i + j + k$.

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