Two vectors $\mathbf{a}$ and $\mathbf{b}$ lie in the same plane with magnitudes $|\mathbf{a}| = 5$ cm and $|\mathbf{b}| = 7$ cm. The vector $\mathbf{c}=\mathbf{a}+2\mathbf{b}$ has magnitude $13$ cm. Determine the angle between $\mathbf{a}$ and $\mathbf{b}$.

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\cos^{-1}\left(-\frac{13}{35}\right)

Neco 2025 Further Mathematics Question 7

Two vectors \(\mathbf{a}\) and \(\mathbf{b}\) lie in the same plane with magnitudes \(|\mathbf{a}| = 5\) cm and \(|\mathbf{b}| = 7\) cm. The vector \(\mathbf{c}=\mathbf{a}+2\mathbf{b}\) has magnitude \(13\) cm. Determine the angle between \(\mathbf{a}\) and \(\mathbf{b}\).

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