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Two forces are equal to 2vec(OA) and 3vec(BO), their resultant being lambda vec(OG), where G is the point on AB such that (BG)/(AG)=-(2)/(3). What is the value of lambda? |
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Answer» 1 `vec(OG)=(2vec(OA)-3vec(OB))/(-1)` `-vec(OG)=2vec(OA)-3vec(OB) " " ...(1)` `lambda vec(OG)=2vec(OA)+3vec(OB) "" ....(2)` ADDING (1) and (2) `(lambda-1)vec(OG)=4vec(OA)` `rArr vec(OA)=((lambda-1)/(4))vec(OG) " " ...(3)` SUBTRACTING(2) from (1) `(-1-lambda)vec(OG)=-6vec(OB)=((1+lambda))/(6)vec(OG) " " ...(4)` From EQU(2), (3) and (4) `lambdavec(OG)=2((lambda-1)/(4))vec(OG)+3((lambda+1)/(6))vec(OG)` `rArr lambda(lambda-1)/(2)=(lambda+1)/(3)` `:. lambda=(lambda-1)/(2) or lambda=(lambda+1)/(3)` `rArr 2lambda-lambda=-1 or 3lambda-lambda=1` `rArr lambda=-1 or lambda=(1)/(2)` |
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