Two vectors (mathbf{a}) and (mathbf{b}) comply with the following conditions: ((i) mathbf{a} cdot mathbf{b}=20 ;() ii ()(mathbf{a}+mathbf{b})
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Two vectors \(\mathbf{a}\) and \(\mathbf{b}\) comply with the following conditions: \((i) \mathbf{a} \cdot \mathbf{b}=20 ;(\) ii \()(\mathbf{a}+\mathbf{b}) \cdot \mathbf{a}=36\); (iii) \((\mathbf{a}+\mathbf{b}) \cdot \mathbf{b}=45\). Determine the magnitude of the two vectors and the angle \(\alpha\) between them.
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