2023 HCI J2 MYE P2 Q3
(a)
Given that $\mathbf{u}$, $\mathbf{v}$ and $\mathbf{w}$ are nonzero vectors such that $\mathbf{u}=\mathbf{v}\times \mathbf{w}$, state the geometric relationship that $\mathbf{u}$ has with $\mathbf{v}$ and $\mathbf{w}$ respectively.
[1]
The vector $\mathbf{r}$ is given as $\mathbf{r}=\mathbf{a}\times \left( \mathbf{b}\times \mathbf{c} \right)$, where $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ are non-zero, non-parallel vectors.
(b)
Explain why $\mathbf{r}$ can be expressed as $\mathbf{r}=\lambda \mathbf{b}+\mu \mathbf{c}$, for constants $\lambda $ and $\mu $.
[2]
(c)
Find the value of $\lambda \mathbf{a}\cdot \mathbf{b}+\mu \mathbf{a}\cdot \mathbf{c}$.
[2]
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