Задача 63638 ...

619d06c90e11ec0cc08e492d

13.03.2022 19:20:49

Дан параллелепипед ABCDA_1B_1C_1D_1; AB = a, AD = b, AA_1 = c. Разложите вектор AM по векторам a, b, c, если M = [D_1 C] ∩ [D C_1]

5f3eaa23faf909182968dde0

13.03.2022 19:44:03

★

АМ=АD+DM=
=AD+(1/2)DC_(1)=
=AD+(1/2)*(AC_(1)-AD)=
=AD+(1/2)AC_(1)-(1/2)AD=
=(1/2)AC_(1)+(1/2)AD=
=(1/2)*(AC_(1)+AD)=
=(1/2)*(a+b+c+b)=(1/2)a+b+(1/2)c.