NYJC 4B Tutorial Q10
(i)
The non-zero vectors $\mathbf{a,b}$ and $\mathbf{c}$ are such that $\mathbf{a}\times \mathbf{b}=\mathbf{c}\times \mathbf{a}$. Given that $\mathbf{b}\ne -\mathbf{c}$, find a linear relationship between $\mathbf{a,b}$ and $\mathbf{c}$.
(ii)
The variable vector $\mathbf{v}$ satisfies the equation $\mathbf{v}\times (\mathbf{i}-3\mathbf{k})=2\mathbf{j}$. Find the set of vectors $\mathbf{v}$ and fully describe this set geometrically.
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