2020 YIJC P1 Q1
Vectors $\mathbf{a}$,$\mathbf{b}$ and $\mathbf{c}$ are such that $\mathbf{b}\ne \mathbf{0}$ and $3\mathbf{a}\times \mathbf{b}=7\mathbf{b}\times \mathbf{c}$.
(i)
Show that $3\mathbf{a}+7\mathbf{c}=\lambda \mathbf{b}$, where $\lambda $ is a constant.
[2]
(ii)
It is now given that $\mathbf{a}$and $\mathbf{b}$ are unit vectors, that the modulus of $\mathbf{c}$ is $\frac{3}{7}$ and that the angle between $\mathbf{a}$ and $\mathbf{c}$ is $60{}^\circ $. Using a suitable scalar product, find exactly the two possible values of $\lambda $.
[4]
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