Geospatial Analytics: Mapping Vector Components on Unit Grids
Geospatial Analytics: Mapping Vector Components on Unit Grids
Secondary 4
Cartesian grid with point A and vector questions
- Draw the column vectors \(\mathbf{a} = \begin{pmatrix} 2 \\ -5 \end{pmatrix}\), \(\overrightarrow{AB} = \begin{pmatrix} -3 \\ 5 \end{pmatrix}\) and \(\overrightarrow{BC} = \begin{pmatrix} 8 \\ 2 \end{pmatrix}\) 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 = (10, 7), C = (18, 9), with the requested vectors drawn on the axes. (ii) |a| = 5.39 units, |AB| = 5.83 units, |BC| = 8.25 units (3 s.f.). (iii) AC = (5, 7)^T.
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