If D,E and F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC and `lambda` is scalar, such that `vec(AD) + 2/3vec(BE)+1/3vec(CF)=lambdavec(AC)`, then `lambda` is equal to

Options

A. `1/2`
B. 1
C. `3//2`
D. 2

Answer

A

Explanation

`vec(AD) + 2/3vec(BE) + 1/3vec(CF)`
`=(vecd-veca)+2/3(vece-vecb)+1/3(vecf-vecc)`
`=1/2(vecc-veca)`
Putting `vecd=(vecb+vecc)/(2), vece=(veca+vecc)/(2), vecf=(veca+vecb)/(2)`
`=1/2(vec(AC))`