8-mavzu. Vektorlarning vektor va aralash ko‘paytmalari reja

> point(A,7,2,2),point(B,5,7,7), point(C,4,6,10), point(D,2,3,7):
> with(LinearAlgebra):
> v := ;

> VectorNorm(v,2,conjugate=false);

> v1 := <5-7,7-2,7-2>;

> VectorNorm(v1,2,conjugate=false);

> Normalize(,Euclidean,conjugate=false);

> Normalize(v1,Euclidean,conjugate=false);

2) (8.8) formuladan , larni hisobga olib, topamiz:

> vAC := <4-7,6-2,10-2>;

> AB.AC:=Dotroduct( <5-7,7-2,7-2>, <4-7,6-2,10-2> );

vektor ko‘paytmani (8.1) formula bilan topamiz:

> A := <||>;

> Determinant(A);
> axb := <||>;

> Determinant(axb);
3) uchburchak yuzasini (8.2) formula bilan hisoblaymiz:

> modN:=VectorNorm(N,2,conjugate=false);
> s:=modN/2;
> with(geom3d):
₄₎ piramida xajmini topamiz:

> abc := <<-5,-2,-3>|<1,5,4>|<5,5,8>>;

> Determinant(abc); -64
> VABCD:={ABC(Determinant(abc))/6};
.


8-AMALIY MASHG’ULOT
8.1. Agar bo‘lsa, quyidagilarni toping:
1) ; 2) .
8.2. Tomonlari va vektorlar uzunliklaridan iborat bo‘lgan parallelogrammning yuzini toping:
1) bu yerda , ,
2) bu yerda , ,
8.3. Agar bo‘lsa, ni toping.
8.4. Agar bo‘lsa, ni toping.
8.5. va vektorlar berilgan. Vektor ko‘paytmalarni toping:
1) ; 2) .
8.6. Tomonlari va vektorlar uzunliklaridan iborat bo‘lgan uchburchakning
yuzini toping: 1) 2)
8.7. Uchburchak uchlari , , berilgan. Uning uchidan
tomonga tushirilgan balandlik uzunligini toping.
8.8. nuqtaga kuch qo‘yilgan. Bu kuchning nuqtaga nisbatan momentini
toping: ) 2)
8.9. kuch qo‘yilgan. nuqtaga nisbatan
kuch momentining qiymatini va yo‘naltiruvchi kosinuslarini toping.