If overline{a}=2 hat{imath}+3 hat{jmath}+hat{ | vedclass

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Question

(A) The position vector of the centroid $G$ of a triangle with vertices having position vectors $\overline{a}$,$\overline{b}$,and $\overline{c}$ is gi

Vedclass · Accepted Answer

$4 \hat{\imath}+3 \hat{\jmath}+3 \hat{k}$

Vedclass · Answer

(A) The position vector of the centroid $G$ of a triangle with vertices having position vectors $\overline{a}$,$\overline{b}$,and $\overline{c}$ is given by the formula: $\overline{g} = \frac{\overline{a} + \overline{b} + \overline{c}}{3}$.Substituting the given vectors:$\overline{g} = \frac{(2 \hat{\imath} + 3 \hat{\jmath} + \hat{k}) + (4 \hat{\imath} + 5 \hat{\jmath} + 3 \hat{k}) + (6 \hat{\imath} + \hat{\jmath} + 5 \hat{k})}{3}$Summing the components:$\overline{g} = \frac{(2+4+6) \hat{\imath} + (3+5+1) \hat{\jmath} + (1+3+5) \hat{k}}{3}$$\overline{g} = \frac{12 \hat{\imath} + 9 \hat{\jmath} + 9 \hat{k}}{3}$$\overline{g} = 4 \hat{\imath} + 3 \hat{\jmath} + 3 \hat{k}$.

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