The Navigator’s Guide: Mapping Vectors on the Grid
The Navigator’s Guide: Mapping Vectors on the Grid
Secondary 4
Cartesian grid with point A and vector questions
- Draw the column vectors \(\mathbf{a} = \begin{pmatrix} -3 \\ 7 \end{pmatrix}\), \(\overrightarrow{AB} = \begin{pmatrix} -4 \\ -2 \end{pmatrix}\) and \(\overrightarrow{BC} = \begin{pmatrix} 5 \\ -1 \end{pmatrix}\) on the \(1\) unit by \(1\) unit square grid provided.
- Find the magnitude of \(\mathbf{a}\), \(\overrightarrow{AB}\) and \(\overrightarrow{BC}\).
- Write down the column vector of \(\overrightarrow{AC}\).
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Answer:(i) B = (9, 7), C = (14, 6), with the requested vectors drawn on the axes. (ii) |a| = 7.62 units, |AB| = 4.47 units, |BC| = 5.10 units (3 s.f.). (iii) AC = (1, -3)^T.
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