A) 0
B) \[\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}\]
C) \[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3}\]
D) \[\frac{\mathbf{a}+\mathbf{b}-\mathbf{c}}{3}\]
Correct Answer: A
Solution :
Position vectors of vertices A, B and C of the triangle ABC = a, b and c. We know that position vector of centroid of the triangle (G) =\[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3}\]. Therefore ,\[\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}\] \[=\left( \mathbf{a}-\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3} \right)+\left( \mathbf{b}-\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3} \right)+\left( \mathbf{c}-\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3} \right)\] \[=\frac{1}{3}[2\mathbf{a}-\mathbf{b}-\mathbf{c}+2\mathbf{b}-\mathbf{a}-\mathbf{c}+2\mathbf{c}-\mathbf{a}-\mathbf{b}]=\mathbf{0}\].You need to login to perform this action.
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