Задача 53649 помощь...

5f6c65a2019fbf2dafd19b19

25.09.2020 12:04:41

помощь

5f3ea7e3faf909182968ddd9

25.09.2020 18:33:00

★

1)
vector{j} ×vector{k}=vector{i}
vector{i} ×vector{k}=-vector{j}
vector{i} × vector{j}=vector{k}

2vector{i} *(vectorj} ×vector{k})+3vector{j} *(vector{i} ×vector{k})+4vector{k}*(vector{i} × vector{j})=

=2vector{i} *vector{i} +3vector{j} *(-vector{j}) +4vector{k}*vector{k}=2-3+4=3

3)
[m]\begin{vmatrix} \vec{i}&\vec{j} &\vec{k} \\ 1&-4 &-5 \\ 2& 6&-1 \end{vmatrix}[/m]=[m]\begin{vmatrix} -4 &-5 \\ 6&-1 \end{vmatrix}\vec{i}-\begin{vmatrix} 1&-5 \\ 2&-1 \end{vmatrix}\vec{j}+\begin{vmatrix} 1&-4 \\ 2& 6\end{vmatrix}\vec{k}=[/m]

[m]=((-4)\cdot (-1)-6\cdot (-5))\vec{i}-(1\cdot (-1)-2\cdot (-5))\vec{j}+(1\cdot 6-2\cdot (-4))\vec{k}=34\vec{i}-9\vec{j}+14\vec{k}[/m]