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Consider the ragular hexagon ABCDEF with centre at O (origin). Five forces vec(AB), vec(AC), vec(AD), vec(AE), vec(AF) act at the vertex A of a regular hexagon ABCDEF. Then their resultant is |
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Answer» ` 3 vec(AO)` `vec(AD) + vec(EB) + vec(FC) = 2 vec(AO) + 2 vec(OB) + 2 vec(OC)` `"" = 2 ( vec(AO) + vec(OB) ) + 2 vec(OC)` `"" = 2 vec(AB) + 2 vec(AB) ` `"" ( because vec(OC) = vec(AB))` `"" = 4 vec(AB)` `vecR = vec(AB) + vec(AC) + vec(AD) + vec(AE) + vec(AF)` `= vec(ED) + vec(AC) + vec(AD) + vec(AE) +vec(CD)` `( because vec(AB) = vec(ED) and vec(AF)= vec(CD))` `= ( vec(AC) + vec(CD)) + ( vec(AE) + vec(ED)) + vec(AD)` `= vec(AD) + vec(AD) + vec(AD) = 3 vec(AD) = 6 vec(AO)` |
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