Question

daca te pricepi la vectori, plss ajuta-ma​

Answer 1

BM, MC, AM, AB, AC sunt vectori.

BM = 2MC

AM = xAB + yAC

AB = AM+MB = AM-BM = AM-2MC

AC = AM+MC

=> AM = x(AM-2MC)+y(AM+MC)

=> AM = xAM-2xMC+yAM+yMC

=> AM = AM(x+y) + MC(-2x+y)

=> x+y = 1, -2x+y = 0 => y = 1-x => -2x+1-x = 0 => -3x = -1 => x = 1/3

=> y = 1 - 1/3 => y = 2/3

=> x = 1/3, y = 2/3

=> AM = (1/3)×AB+(2/3)×AC