Asosiy tarkibga o'tish

11.4-bo'lim : O'zaro mahsulot

2. Agar \(\vec w = \left\langle {1,6, - 8} \right\rangle \) va \(\vec v = \left\langle {4, - 2, - 1} \right\rangle \) \(\vec w \times \vec v\) hisoblansa.

Yechim

Bu erda juda ko'p narsa qilish kerak emas. Biz shunchaki ko'ndalang mahsulotni hisoblashning turli usullaridan birini ishlatishimiz kerak. Biz eslatmalarda ishlatgan "hiyla" dan foydalanamiz.

\[\begin{align*}\vec w \times \vec v & = \left| {\begin{array}{*{20}{c}}{\vec i}&{\vec j}&{\vec k}\\1&6&{ - 8}\\4&{ - 2}&{ - 1}\end{array}} \right|\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{\vec i}&{\vec j}\\1&6\\4&{ - 2}\end{array}\\ & = - 6\vec i - 32\vec j - 2\vec k - \left( { - \vec j} \right) - 16\vec i - 24\vec k = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 22\vec i - 31\vec j - 26\vec k}}\end{align*}\]