In a plane, vectors $\mathbf{a}$ and $\mathbf{b}$ satisfy $|\mathbf{a}| = 5$, $|\mathbf{b}| = 4$ and $\mathbf{a}\cdot\mathbf{b} = 12$. Determine (i) the magnitude of $\mathbf{a} - 2\mathbf{b}$ and (ii) the angle between $\mathbf{a}$ and $\mathbf{a} - 2\mathbf{b}$.

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Accepted Answer

|\mathbf{a} - 2\mathbf{b}| = \sqrt{41}, 	heta = \arccos\left(\frac{1}{5\sqrt{41}}ight)

Gce Model Questions Vol1 2018 Mathematics Question 13

In a plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 4\) and \(\mathbf{a}\cdot\mathbf{b} = 12\). Determine (i) the magnitude of \(\mathbf{a} - 2\mathbf{b}\) and (ii) the angle between \(\mathbf{a}\) and \(\mathbf{a} - 2\mathbf{b}\).

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