 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-1/10/b/solution

The dot product formula for the angle between two nonzero vectors gives

cos ∠ A OB = \frac{( 3 , 4 ) \cdot ( 5 , 12 )}{5 \cdot 13} = \frac{15 + 48}{65} = \frac{63}{65} .

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