а=2p+3q
b=p–2q
|p|=3 |q|=1
Угол фи равен п/3
=[2* vector{p} × vector{p}]+[3* vector{q} × vector{p}]+[2 *vector{p} × (-2)* vector{q}]+[3* vector{q} × (-2) *vector{q}]=
=2 [vector{p} × vector{p}]+3 [vector{q} × vector{p}]-4[ vector{p} × vector{q}]-6[ vector{q} × vector{q}]=
по свойству векторного произведения векторов: [r] [vector{q} × vector{p}]=-[ vector{p} × vector{q}][/r]
=2 [vector{p} × vector{p}]+3(-[vector{p} × vector{q}]-4[ vector{p} × vector{q}]-6[ vector{q} × vector{q}]=
=2 [vector{p} × vector{p}]-7[vector{p}] × vector{q}-6[ vector{q} × vector{q}]
|[vector{a} × vector{b}]|=|2|*|vector{p}|*| vector{p}|*sin0+|-7|* |vector{p}|* |vector{q}|*sin(π/3)+|-6||vector{q}|*|vector{q}}*sin0=
=2*3*3*0+7*3*1*(sqrt(3)/2)+6*1*1*0=[b]21sqrt(3)/2[/b]
S_( параллелограмма)=|[vector{a} × vector{b}]|=[b]21sqrt(3)/2[/b]