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Question Number 118280 by hmh2k20 last updated on 16/Oct/20

$$\left(26\right)\overrightarrow{\mathrm{OA}}=\overrightarrow{\mathrm{a}}=\left(\begin{array}{c}4.8\\ 3.6\end{array}\right),\overrightarrow{\mathrm{OB}}=\overrightarrow{\mathrm{b}}=\left(\begin{array}{c}8\\ 15\end{array}\right)$$$$\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}=(4.8)\left(8\right)+(3.6)\left(15\right)=92.\overrightarrow{4}$$$$\mathrm{a}=\sqrt{4.8^2+3.6^2}=\sqrt{23.04+12.96}=\sqrt{36}=6$$$$\mathrm{b}=\sqrt{8^2+{15}^2}=\sqrt{64+225}=\sqrt{289}=17$$$$\mathrm{a}.\mathrm{b}=6.17=102$$$$\cos \mathrm{AOB}=\frac{\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}}{\mathrm{a}.\mathrm{b}}=\frac{92.4}{102}=0.9059=\cos 25.06°$$$$\therefore \mathrm{\angle }\mathrm{AOB}=25.06°$$

Commented by Ar Brandon last updated on 16/Oct/20

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