A grid vector in terms of u and v
A grid vector in terms of u and v
Secondary 4
4 marks
The diagram shows the vectors \(\mathbf{u}\) and \(\mathbf{v}\) and the points \(A\) and \(B\) on a 1 unit by 1 unit grid.
- Express \(\overrightarrow{AB}\) in terms of \(\mathbf{u}\) and \(\mathbf{v}\).[2]
- Check your answer by writing \(\mathbf{u}\), \(\mathbf{v}\) and \(\overrightarrow{AB}\) as column vectors.[2]
Solution:
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Answer:(a) \(\overrightarrow{AB}=2\mathbf{u}+2\mathbf{v}\) (b) \(2\begin{pmatrix}2\\ 3\end{pmatrix}+2\begin{pmatrix}2\\ -1\end{pmatrix}=\begin{pmatrix}8\\ 4\end{pmatrix}=\overrightarrow{AB}\)
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