11.3-bo'lim : Nuqta mahsuloti
9. Berilgan \(\vec a = \left\langle { - 8,2} \right\rangle \) va \(\vec b = \left\langle { - 1, - 7} \right\rangle \) \({{\mathop{\rm proj}\nolimits} _{\,\vec a}}\,\vec b\) ni hisoblaydi.
Yechim
Bu erda biz qilishimiz kerak bo'lgan yagona narsa eslatmalardan formuladan foydalanishdir. Buning uchun quyidagi miqdorlar kerak bo'ladi.
\[\vec a\centerdot \vec b = - 6\hspace{0.25in}\hspace{0.25in}{\left\| {\vec a} \right\|^2} = 68\]Keyin proyeksiya,
\[{{\mathop{\rm proj}\nolimits} _{\,\vec a}}\,\vec b = \frac{{ - 6}}{{68}}\left\langle { - 8,2} \right\rangle = \require{bbox} \bbox[2pt,border:1px solid black]{{\left\langle {\frac{{12}}{{17}}, - \frac{3}{{17}}} \right\rangle }}\]