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Addition of Vectors

If G is the...

Question

If $G$ is the centroid of a $Δ A B C$ , then $\to G A + \to G B + \to G C$ is equal to

A

\to 0

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B

3 \to G A

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C

3 \to G B

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D

3 \to G C

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Solution

The correct option is A $\to 0$
We have $\to G B + \to G C = (1 + 1) \to G D = 2 \to G D$ , where $D$ is the midpoint of $B C$ . Therefore,
$\to G A + \to G B + \to G C = \to G A + 2 \to G D$
$= \to G A - \to G A = 0$
$(∵ G$ divides $A C$ in the ration $2 : 1, ∴ 2 \to G D = - \to G A)$

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