2016 RI Promo Q2
2016 RI Promo Q2
3 marks
Promo
The variable vector \(\mathbf{v}\) satisfies the equation \(\mathbf{v}\cdot \left( 2\mathbf{j}+\mathbf{k} \right)=0\) and \(\mathbf{v}\cdot \left( 3\mathbf{i}+7\mathbf{k} \right)=0\).
- Find the set of vectors \(\mathbf{v}\).[2]
- Describe geometrically the set of points with position vectors found in part (i).[1]
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Answer:(i) \(\displaystyle \mathbf{v}=\lambda\begin{pmatrix}14\\3\\-6\end{pmatrix}\), \(\lambda\in\mathbb{R}\) (ii) A line through the origin parallel to \(\begin{pmatrix}14\\3\\-6\end{pmatrix}\)
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