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

Question

Given that column vectors $\mathbf{a} = \begin{pmatrix} -6 \ 2 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 10 \ 6 \end{pmatrix}$. Draw, on the $1$ unit by $1$ unit square grid provided, the relationship between $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{a} + \mathbf{b}$. Find the column vector of $\mathbf{a} + \mathbf{b}$ numerically. Find the value of $|\mathbf{a}|$, $|\mathbf{b}|$ and $|\mathbf{a} + \mathbf{b}|$. Is $|\mathbf{a} + \mathbf{b}| = |\mathbf{a}| + |\mathbf{b}|$? Explain your answer.

Accepted 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

Vector Addition and Resultant Analysis

Vector Addition and Resultant Analysis

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