Given that column vectors $\mathbf{a} = \begin{pmatrix} -3 \ 7 \end{pmatrix}$ and \(\mathbf{b} =

Question

Given that column vectors $\mathbf{a} = \begin{pmatrix} -3 \ 7 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 5 \ -2 \end{pmatrix}$. 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 with $-\mathbf b$ (ii) $\begin{pmatrix}-8\9\end{pmatrix}$ (iii) $\lvert\mathbf a\rvert=\sqrt{58}\approx7.62,\ \lvert\mathbf b\rvert=\sqrt{29}\approx5.39,\ \lvert\mathbf a-\mathbf b\rvert=\sqrt{145}\approx12.0$ (iv) No

Arithmetic of Column Vectors: Subtraction and Resultants

Arithmetic of Column Vectors: Subtraction and Resultants

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