11.4-bo'lim : O'zaro mahsulot
1. Agar \(\vec w = \left\langle {3, - 1,5} \right\rangle \) va \(\vec v = \left\langle {0,4, - 2} \right\rangle \) \(\vec v \times \vec w\) 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.
\[\begin{align*}\vec v \times \vec w & = \left| {\begin{array}{*{20}{c}}{\vec i}&{\vec j}&{\vec k}\\0&4&{ - 2}\\3&{ - 1}&5\end{array}} \right|\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{\vec i}&{\vec j}\\0&4\\3&{ - 1}\end{array}\\ & = 20\vec i - 6\vec j + 0\vec k - 0\vec j - 2\vec i - 12\vec k = \require{bbox} \bbox[2pt,border:1px solid black]{{18\vec i - 6\vec j - 12\vec k}}\end{align*}\]