11.3-bo'lim : Nuqta mahsuloti
3. Agar \(\left\| {\vec a} \right\| = 5\), \(\displaystyle \left\| {\vec b} \right\| = \frac{3}{7}\) va ikki vektor orasidagi burchak \(\displaystyle \theta = \frac{\pi }{{12}}\) bo‘lsa, nuqta hosilasi, \(\vec a\centerdot \vec b\)ni aniqlang.
Yechim
Bu erda juda ko'p narsa qilish kerak emas. Biz faqat nuqta mahsulotining geometrik talqinidan formuladan o'tishimiz kerak.
\[\vec a\centerdot \vec b = \left( 5 \right)\left( {\frac{3}{7}} \right)\cos \left( {\frac{\pi }{{12}}} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{2.0698}}\]