Answer:
I have four possible answers:
1. [tex]\begin{pmatrix}5&6\end{pmatrix}\begin{pmatrix}7&12\end{pmatrix}=107[/tex]
2. [tex]\mathrm{Computing\:the\:angle\:between\:}\begin{pmatrix}5&6\end{pmatrix}\mathrm{\:and\:}\begin{pmatrix}7&12\end{pmatrix}:\quad 9.54913\dots ^{\circ[/tex]
3. [tex]\mathrm{Computing\:the\:projection\:of\:}\begin{pmatrix}7&12\end{pmatrix}\mathrm{\:onto\:}\begin{pmatrix}5&6\end{pmatrix}:\quad \begin{pmatrix}\frac{535}{61}&\frac{642}{61}\end{pmatrix}[/tex]
4.[tex]\mathrm{Computing\:the\:scalar\:projection\:of\:}\begin{pmatrix}7&12\end{pmatrix}\mathrm{\:onto\:}\begin{pmatrix}5&6\end{pmatrix}:\quad \frac{107\sqrt{61}}{61}[/tex]
at 15y-90=225 (not sure)
Step-by-step explanation:
2.[tex]\mathrm{Computing\:dot\:product\:of\:two\:vectors}:[/tex][tex]\left(x_1,\:\:\ldots ,\:\:x_n\right)\cdot \left(y,\:\:\ldots ,\:\:y_n\right)=\sum _{i=1}^nx_iy_i[/tex]
[tex]\cos \left(θ\right)=\frac{107}{\sqrt{11773}}[/tex][tex]θ=\arccos \left(\cos \left(θ\right)\right)=\arccos \left(\frac{107\sqrt{11773}}{11773}\right)[/tex] =[tex]9.54913\dots ^{\circ \:}[/tex]
1.[tex]=5\cdot \:7+6\cdot \:12[/tex] simplify = 107
