In an octagon ABCDEFGH of equal side, what is the sum of AB→$$+AC$$→$$+AD$$→$$+AE$$→$$+AF$$→$$+AG$$→$$+AH$$→, If AO→$$=2i^+3j^$$−$$4k^$$

Question

In an octagon ABCDEFGH of equal side, what is the sum of AB→$$+AC$$→$$+AD$$→$$+AE$$→$$+AF$$→$$+AG$$→$$+AH$$→,  If AO→$$=2i^+3j^$$−$$4k^$$

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Let say OA→$$=a$$→ , OB→$$=b$$→, OC→$$=c$$→, OD→$$=d$$→, OE→$$=e$$→, OF→$$=f$$→, OG→$$=g$$→, OH→$$=h$$→Due to symmetry, a→$$+b$$→$$+c$$→$$+d$$→$$+e$$→$$+f$$→$$+g$$→$$+h$$→$$=0$$⇒b→$$+c$$→$$+d$$→$$+c$$→$$+f$$→$$+g$$→$$+h$$→$$=-a$$→Now, AB→$$+AC$$→$$+AD$$→$$+AE$$→$$+AF$$→$$+AG$$→$$+AH$$→            $$=b$$→$$-a$$→$$+c$$→$$-a$$→$$+d$$→$$-a$$→$$+e$$→$$-a$$→$$+f$$→$$-a$$→$$+g$$→$$-a$$→$$+h$$→$$-a$$→            $$=b$$→$$+c$$→$$+d$$→$$+e$$→$$+f$$→$$+g$$→$$+h$$→$$-7a$$→            $$=-a$$→$$-7a$$→$$=-8a$$→            $$=-8(OA$$→$$)=-8$$×$$-2i^-3j^+4k^$$            $$=16i^+24j^-32k^$$

In an octagon ABCDEFGH of equal side, what is the sum of $\vec{A B} + \vec{A C} + \vec{A D} + \vec{A E} + \vec{A F} + \vec{A G} + \vec{A H},$ If $\vec{A O} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$

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In an octagon ABCDEFGH of equal side, what is the sum of AB→+AC→+AD→+AE→+AF→+AG→+AH→, If AO→=2i^+3j^−4k^

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In an octagon ABCDEFGH of equal side, what is the sum of $\vec{A B} + \vec{A C} + \vec{A D} + \vec{A E} + \vec{A F} + \vec{A G} + \vec{A H},$ If $\vec{A O} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$