Three non‑zero vectors $\mathbf{a},\mathbf{b},\mathbf{c}$ in space satisfy $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}$. Given $|\mathbf{a}|=3$, $|\mathbf{b}|=4$ and $\mathbf{a}\cdot\mathbf{b}=6$, find $|\mathbf{c}|$ and the angle between $\mathbf{b}$ and $\mathbf{c}$.

Question

Three non‑zero vectors $\mathbf{a},\mathbf{b},\mathbf{c}$ in space satisfy $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}$.  Given $|\mathbf{a}|=3$, $|\mathbf{b}|=4$ and $\mathbf{a}\cdot\mathbf{b}=6$, find $|\mathbf{c}|$ and the angle between $\mathbf{b}$ and $\mathbf{c}$.

Accepted Answer

|c| = \sqrt{37}, angle = \arccos\left(-\frac{11}{2\sqrt{37}}\right)

Neco 2018 Further Mathematics Question 28

Three non‑zero vectors \(\mathbf{a},\mathbf{b},\mathbf{c}\) in space satisfy \(\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\). Given \(|\mathbf{a}|=3\), \(|\mathbf{b}|=4\) and \(\mathbf{a}\cdot\mathbf{b}=6\), find \(|\mathbf{c}|\) and the angle between \(\mathbf{b}\) and \(\mathbf{c}\).

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