АВ = b, AD = d, AC = c, DN = ?
знак вектора не ставлю.
DN = 1/2(DA + DM) = 1/2(-d + DM)
DM = 1/2(DB + DC) = 1/2DB + 1/2 DC
DB = AB - AD= b - d DC = AC - AD= c - d
DN = 1/2(DA + DM) = 1/2(-d + DM)= - 1/2d + 1/2 DM=
= -1/2 d + 1/2( 1/2DB + 1/2 DC) = -1/2 d + 1/4DB + 1/4 DC=
= -1/2 d + 1/4(AB - AD) + 1/4(AC -AD) = -1/2 d + 1/4AB - 1/4 AD + 1/4AC - 1/4AD=
= -1/2 d + 1/4 b - 1/4 d + 1/4с - 1/4d = -d + 1/4 b + 1/4 c