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`?

Options

A. 1
B. -1
C. 2
D. None of the above

Answer

B

Explanation

`vec(OG)=(2vec(OA)-3vec(OB))/(2-3)`
`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)`