If D and E are the midpoints of the sides BA and BC of triangle ABC, then AE + DC =

Step-by-step solution

Using the triangle law of vector addition: AE = AB + BE DC = DB + BC Since D is the midpoint of BA, DB = 1 2 AB . Since E is the midpoint of BC, BE = 1 2 BC . Substituting these into the expressions for AE and DC : AE + DC = ( AB + 1 2 BC ) + ( 1 2 AB + BC ) AE + DC = 3 2 AB + 3 2 BC AE + DC = 3 2 ( AB + BC ) By the triangle law of vector addition, AB + BC = AC . AE + DC = 3 2 AC Answer: 3 2 AC