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Question Number 118277 by hmh2k20 last updated on 16/Oct/20

$$\left(23\right)\mathrm{Let}\overrightarrow{\mathrm{a}}=\left(\begin{array}{c}7\\ 24\end{array}\right)\mathrm{and}\overrightarrow{\mathrm{b}}=\left(\begin{array}{c}3\\ -4\end{array}\right)$$$$\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}=\left(7\right)\left(3\right)+\left(24\right)(-4)=21-96=-75$$$$\mathrm{a}=\sqrt{7^2+{24}^2}=\sqrt{49+576}=\sqrt{625}=25$$$$\mathrm{b}=\sqrt{3^2+{(-4)}^2}=\sqrt{9+16}=\sqrt{25}=5$$$$\mathrm{a}.\mathrm{b}=25.5=125$$$$\mathrm{Let}\theta \mathrm{be}\mathrm{the}\mathrm{angle}\mathrm{between}\overrightarrow{\mathrm{a}}\mathrm{and}\overrightarrow{\mathrm{b}}.$$$$\cos \theta =\frac{\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}}{\mathrm{a}.\mathrm{b}}=\frac{-75}{125}=-0.6=\cos 126.87°$$$$\therefore \theta =126.87°$$

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