Question

ABCD is a parallelogram. If L and M are the
mid points of BC and DC respectively and
->
AL + AM = \AC then 4) =​

Answer 1

Take A as origin.

Let

a , b be the position vectors of the points B,D respectively.

Then,

AB = a and AD = b

By parallelogram law of addition of vectors,

AC = AB + AD

⇒ AC = a + b

∴ The position vector of C is a + b .

Since, L,M are mid-points of BC, and DC respectively.

The position vector of = a + ( a + b )

2

2 a + b

2

AL = 22 a + b

= a + 2b

= AB + 21 AD

⇒ AL + AM =

$(a+21b)+(21a+b)$

= AL + AM = 2/3 AC