Задача 62714 ...

61aded033504e8547126be81

19.01.2022 19:08:20

Векторное и смешанное произведение векторов

Если m=9, n=8 и

[ma + b, 2a - nb] = μ[a, b], то μ =

5f3ea7e3faf909182968ddd9

20.01.2022 10:33:26

★

[(9* vector{a}+ vector{b}) , (2* vector{a}-8* vector{b})]=

=[9* vector{a} , 2* vector{a}]+[ vector{b} , 2* vector{a}]+[9*vector{a} × (-8)* vector{b}]+[ vector{b} × (-8) *vector{b}]=

=18 [vector{a} , vector{a}]+2 [vector{b} , vector{a}]-72[ vector{a} , vector{b}]-8[ vector{b} , vector{b}]=

по свойству векторного произведения векторов: [r] [vector{b} × vector{a}]=-[ vector{a} × vector{b}][/r]


=18 [vector{a}, vector{a}]-74 [vector{a} , vector{b}]-8[ vector{b} , vector{b}]=

по свойству векторного произведения векторов: [r] [vector{a} × vector{b}]=[ vector{b} × vector{b}]=0[/r]

=-74 [vector{a} , vector{b}]