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Sagot :
The vector for (-9,-8) is,
[tex]u=-9\hat{i}-8\hat{j}[/tex]The vector for (-9,5) is,
[tex]v=-9\hat{i}+5\hat{j}[/tex]The formula for the angle between vector u and vector v is,
[tex]\cos \theta=\frac{u\cdot v}{|u\mleft\Vert v\mright|}[/tex]Determine the angle between vectors.
[tex]\begin{gathered} \cos \theta=\frac{(-9\hat{i}-8\hat{j)}\cdot(-9\hat{i}+5\hat{j})}{\sqrt[]{(-9)^2+(-8)^2}\cdot\sqrt[]{(-9)^2+(5)^2}} \\ =\frac{81-40}{\sqrt[]{145}\cdot\sqrt[]{106}} \\ =\frac{41}{\sqrt[]{15370}} \\ \theta=\cos ^{-1}(0.3307) \\ =70.688 \\ \approx71 \end{gathered}[/tex]So angle between the vector is 71 degree.
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