Let G be the centroid of - A B C - If A- -B- - a- - A- -C- - vec b then A- -G- - in terms of a- and b- - is

Take A as origin, then positive vector of A, B, C are given by 0⃗, a⃗, b⃗ respectively, then the centroid G has position vector as =0⃗+a⃗+b⃗3=a⃗+b⃗3 ...

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Standard IX

Mathematics

The Mid-Point Theorem

Let G be th...

Question

Let $G$ be the centroid of $Δ A B C .$ If $\to A B = \to a, \to A C = v e c b$ then $\to A G,$ in terms of $\to a$ and $\to b,$ is

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Solution

Take A as origin, then positive vector of A, B, C are given by $\to 0, \to a, \to b$ respectively, then the centroid G has position vector as $= \frac{\to 0 + \to a + \to b}{3} = \frac{\to a + \to b}{3}$ .

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Let G be the centroid of ΔABC. If →AB=→a,→AC= vec b then →AG, in terms of →a and →b, is

Take A as origin, then positive vector of A, B, C are given by →0,→a,→b respectively, then the centroid G has position vector as =→0+→a+→b3=→a+→b3.

Let $G$ be the centroid of $Δ A B C .$ If $\to A B = \to a, \to A C = v e c b$ then $\to A G,$ in terms of $\to a$ and $\to b,$ is

Take A as origin, then positive vector of A, B, C are given by $\to 0, \to a, \to b$ respectively, then the centroid G has position vector as $= \frac{\to 0 + \to a + \to b}{3} = \frac{\to a + \to b}{3}$ .