Задача 30619 ...

sova

2018-10-29 18:23:10

vector{a}×vector{b}=(3vector{p}+vector{q})×(vector{p}-3vector{q})=

=3vector{p}×vector{p}+vector{q}×vector{p}-9vector{p}×vector{q}-3vector{q}×vector{q}=

так как
vector{p}×vector{p}=vector{q}×vector{q}=0,
vector{p}×vector{q}=-vector{q}×vector{p}, то

получим
=-10vector{p}×vector{q}

S=|vector{a}×vector{b}|=|-10vector{p}×vector{q}|=

=10*|vector{p}|*|vector{q}|*sin ( vector{p},vector{q})=

=10*7*2*sqrt(2)/2=70sqrt(2)
О т в е т. 70sqrt(2)