In three‑dimensional space, vectors $\mathbf{a}$ and $\mathbf{b}$ satisfy $|\mathbf{a}| = 5$, $|\mathbf{b}| = 3$ and $\mathbf{a}\cdot\mathbf{b}=6$. Find (i) the magnitude of $\mathbf{c}=2\mathbf{a}-\mathbf{b}$ and (ii) the cosine of the angle between $\mathbf{a}$ and $\mathbf{c}$.

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\sqrt{85}, \frac{44}{5\sqrt{85}}

Gce Model Questions Vol1 2020 Further Mathematics Question 47

In three‑dimensional space, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 3\) and \(\mathbf{a}\cdot\mathbf{b}=6\). Find (i) the magnitude of \(\mathbf{c}=2\mathbf{a}-\mathbf{b}\) and (ii) the cosine of the angle between \(\mathbf{a}\) and \(\mathbf{c}\).

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