22.2 Adding and subtracting vectors — Practise with help

1. Move 2 right and 3 down.
2. $\begin{pmatrix}3-1\\-2-4\end{pmatrix}=\begin{pmatrix}2\\-6\end{pmatrix}$; subtract start from end.

Add the top entries and the lower entries separately.

$\begin{pmatrix}4+(-2)\\1+5\end{pmatrix}$.

$\begin{pmatrix}2\\6\end{pmatrix}$.

Subtract matching components.

$\begin{pmatrix}7-2\\-3-4\end{pmatrix}$.

$\begin{pmatrix}5\\-7\end{pmatrix}$.

Multiply both entries by 3.

$\begin{pmatrix}3(-2)\\3(1)\end{pmatrix}$.

$\begin{pmatrix}-6\\3\end{pmatrix}$.

Scale the first vector before adding.

$\begin{pmatrix}6\\-2\end{pmatrix}+\begin{pmatrix}-4\\5\end{pmatrix}$.

$\begin{pmatrix}2\\3\end{pmatrix}$.

What vector reverses the direction of $\mathbf{b}$?

$-\mathbf{b}$ has the same length and the opposite direction.

Adding $-\mathbf{b}$ undoes the movement $\mathbf{b}$, so it gives the same result as subtracting $\mathbf{b}$.

Reverse the whole route.

Reverse each movement and reverse the order: $-\mathbf{v}-\mathbf{u}$.

$\overrightarrow{CA}=-\mathbf{u}-\mathbf{v}$, which is the negative of $\overrightarrow{AC}$.