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A B C D parallelogram, and A1a n dB1 are...

`A B C D` parallelogram, and `A_1a n dB_1` are the midpoints of sides `B Ca n dC D ,` respectivley . If ` vec A A_1+ vec A B_1=lambda vec A C ,t h e nlambda` is equal to a. `1/2` b. `1` c. `3/2` d. `2` e. `2/3`

A

`(1)/(2)`

B

`1`

C

`(3)/(2)`

D

`2 `

Text Solution

Verified by Experts

The correct Answer is:
C

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)`
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