Vector Addition and Resultant Analysis

Vector Addition and Resultant Analysis

Secondary 4
Square grid with x and y axes
Square grid with x and y axes

Given that column vectors \(\mathbf{a} = \begin{pmatrix} -6 \\ 2 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} 10 \\ 6 \end{pmatrix}\).

  1. Draw, on the \(1\) unit by \(1\) unit square grid provided, the relationship between \(\mathbf{a}\), \(\mathbf{b}\) and \(\mathbf{a} + \mathbf{b}\).
  2. Find the column vector of \(\mathbf{a} + \mathbf{b}\) numerically.
  3. Find the value of \(|\mathbf{a}|\), \(|\mathbf{b}|\) and \(|\mathbf{a} + \mathbf{b}|\).
  4. Is \(|\mathbf{a} + \mathbf{b}| = |\mathbf{a}| + |\mathbf{b}|\)? Explain your answer.

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Answer:(i) Head-to-tail construction (ii) \(\begin{pmatrix}4\\8\end{pmatrix}\) (iii) \(\lvert\mathbf a\rvert=2\sqrt{10}\approx6.32,\ \lvert\mathbf b\rvert=2\sqrt{34}\approx11.7,\ \lvert\mathbf a+\mathbf b\rvert=4\sqrt5\approx8.94\) (iv) No

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