The non-zero vectors $\mathbf{a,b}$ and $\mathbf{c}$ are such that $\mathbf{a} imes \mathbf{b}=\mat

Question

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

Accepted Answer

(a) $\mathbf{a} = k(\mathbf{b} + \mathbf{c})$ where $k$ is a constant (b) $\left\{ \mathbf{v} = \begin{pmatrix} a \\ 0 \\ 2-3a \end{pmatrix}; a \in \mathbb{R} \right\}$ Geometrical interpretation: Points on the $x$-$z$ plane

NYJC 4B Tutorial Q10

NYJC 4B Tutorial Q10

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