ABCD a parallelogram, and `A_1 and B_1` are the midpoints of sides BC and CD, respectively. If `vec(A A)_1` `+ vec(AB)_1 = lamda vec(AC)`, then `lamda` is equal to `

Options

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

Answer

C

Explanation

Ler P.V. of A, B and D be `vec0, vecb and vecd`, respectively.
Then P.V. of C, `vecc=vecb+ vecd`
Also P.V of `A_1= vecb+ (vecd)/(2) `
and P.V of `B_1 = vecd + (vecb)/(2)`
`rArr vec(AA)_1 + vec(AB)_1 = (3)/(2) (vecb + vecd) = (3)/(2) vec(AC)`