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

Question

Given that column vectors $\mathbf{a}=\begin{pmatrix} -3 \ 7 \end{pmatrix}$ and $\mathbf{b}=\begin{pmatrix} 5\ -4 \end{pmatrix}$. 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) $\begin{pmatrix}2\3\end{pmatrix}$ (iii) $\lvert\mathbf a\rvert=\sqrt{58}\approx7.62,\ \lvert\mathbf b\rvert=\sqrt{41}\approx6.40,\ \lvert\mathbf a+\mathbf b\rvert=\sqrt{13}\approx3.61$ (iv) No

Vector Addition and Geometric Representation

Vector Addition and Geometric Representation

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