НОМЕР 3.67 ПОЛНОСТЬЮ
НОМЕР 3.68(1,4)
3.67
1)
vector{a} *vector{a} =|vector{b}| *|vector{a}|* cos φ =3*sqrt(2)*cos45^(o)=
=3*sqrt(2)*(sqrt(2)/2)=3
2)
vector{a} *vector{a} =|vector{b}| *|vector{a}|* cos φ =0,5*16*cos60^(o)
=0,5*16*0,5=4
3)
vector{a} *vector{a} =|vector{b}| *|vector{a}|* cos φ=
=sqrt(3)*3*cos30^(o)=sqrt(3)*3*(sqrt(3)/2)=4,5
4)vector{a} *vector{a} =|vector{b}| *|vector{a}|* cos φ
=4*3*cos120^(o)=4*3*(-0,5)=-6
3.68
vector{a}×vector{b}=a_(1)*b_(1)+a_(2)*b_(2)+a_(3)*b_(3)=
=2*1-1*sqrt*(2)+0*(-5)=2-2sqrt(2)
4)
(vector{a}-vector{b})*(vector{a}+vector{c})=
= применяем законы векторной [b]алгебры[/b]=
=vector{a}*vector{a}-vector{b}*vector{a} +vector{a}*vector{c}-vector{b}*vector{c}
=([blue]2*2+(-1)*(-1)+0*0[/blue])-(1*2+sqrt(2)*(-1)+(-5)*0)+([blue]2*1+(-1)*2+0*5[/blue])-(1*1+sqrt(2)*2+(-5)*5)=