2023 NJC Promo Q5
(b)
Two non-zero vectors $\mathbf{a}$ and $\mathbf{b}$ are such that $\left| \mathbf{a}\times \mathbf{b} \right|=\sqrt{3}$, $\left| \mathbf{a}-\mathbf{b} \right|=1$ and the angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is ${{30}^{\circ }}$, find the possible values of $\left| \mathbf{a} \right|$ and $\left| \mathbf{b} \right|$.
[5]
(c)
Two fixed points $C$ and $D$ have position vectors $\mathbf{c}$ and $\mathbf{d}$ respectively. By considering the result $\mathbf{c}\times \mathbf{c}=\mathbf{0}$, give a geometrical interpretation of the vector equation $\mathbf{r}\times \left( \mathbf{d}-\mathbf{c} \right)=\mathbf{c}\times \mathbf{d}$.
[3]
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