Задача 74138 Смешанное произведение векторов...
Условие
Решение
[vector{a},vector{b}]=|vector{a}|*|vector{b}|*sin (vector{a},vector{b})=2*3*sin(π/3)=6*(sqrt(3)/2)=[b]3sqrt(3)[/b]
2)
[2vector{a}-3vector{b}, 5vector{a}+vector{b}]=2*5*[vector{a},vector{a}]-15*[vector{b},vector{a}]+2*[vector{a},vector{b}]-3*[vector{b},vector{b}]=
( по свойству 1: [vector{b},vector{a}]=-[vector{a},vector{b}])
=10*[vector{a},vector{a}]+15*[vector{a},vector{b}]+2*[vector{a},vector{b}]-3*[vector{b},vector{b}]=
=10*[vector{a},vector{a}]+17*[vector{a},vector{b}]-3*[vector{b},vector{b}]=
(по свойству 4)
=10*0+17*[vector{a},vector{b}]-3*0=17*[vector{a},vector{b}]
|[2vector{a}-3vector{b}, 5vector{a}+vector{b}]|=|17*[vector{a},vector{b}]|=
=17*|vector{a}|*|vector{b}|*sin (vector{a},vector{b})=17*2*3*sin(π/3)=102*(sqrt(3)/2)=[b]51sqrt(3)[/b]
3)
[vector{a}, vector{b}+vector{a}]=[vector{a},vector{b}]+[vector{a},vector{a}]=[vector{a},vector{b}]+0=[vector{a},vector{b}]
|[vector{a}, vector{a}+vector{b}]|=|[vector{a},vector{b}]|=|vector{a}|*|vector{b}|*sin (vector{a},vector{b})=2*3*sin(π/3)=6*(sqrt(3)/2)=[b]3sqrt(3)[/b]
