2020 YIJC P1 Q1

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Timothy Gan

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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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Published: 21st June 2022

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