Vectors $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ are such that \(\mathbf{a}\ne \mathbf

Question

Vectors $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ are such that $\mathbf{a}\ne \mathbf{0}$ and $\mathbf{a}\times 3\mathbf{b}=2\mathbf{a}\times \mathbf{c}$. Show that $3\mathbf{b}-2\mathbf{c}=\lambda \mathbf{a}$, where $\lambda $ is a constant.[2] It is now given that $\mathbf{a}$ and $\mathbf{c}$ are unit vectors, that the modulus of $\mathbf{b}$ is $4$ and that the angle between $\mathbf{b}$ and $\mathbf{c}$ is $60{}^\circ $. Using a suitable scalar product, find exactly the two possible values of $\lambda $.[5]

Accepted Answer

(ii) $\lambda =\pm 2\sqrt{31}$

N2018 P1 Q6

N2018 P1 Q6

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