Another grid vector in terms of u and v
Another 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) \(\overrightarrow{AB}=3\mathbf{u}+\mathbf{v}\) (b) \(3\begin{pmatrix}2\\ 1\end{pmatrix}+\begin{pmatrix}1\\ -2\end{pmatrix}=\begin{pmatrix}7\\ 1\end{pmatrix}\)
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