Vectors $\mathbf{a}$ and $\mathbf{b}$ satisfy $|\mathbf{a}|=3$, $|\mathbf{b}|=4$ and $\mathbf{a}\cdot\mathbf{b}=6$. Compute (i) the magnitude of $\mathbf{a}-2\mathbf{b}$ and (ii) the cosine of the angle between $\mathbf{a}-2\mathbf{b}$ and $\mathbf{a}$.

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Magnitude = 7, \cos	heta = -\frac{1}{7}

Neco 2018 Further Mathematics Question 19

Vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}|=3\), \(|\mathbf{b}|=4\) and \(\mathbf{a}\cdot\mathbf{b}=6\). Compute (i) the magnitude of \(\mathbf{a}-2\mathbf{b}\) and (ii) the cosine of the angle between \(\mathbf{a}-2\mathbf{b}\) and \(\mathbf{a}\).

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