Question

20 \\( \overrightarrow{pq} = \

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

\\) and \\( \overrightarrow{qr} = \

$$\begin{pmatrix} 4 \\\\ 1 \\end{pmatrix}$$

\\).
work out \\( \overrightarrow{pr} \\).

Explanation:

Step1: Recall vector addition rule

$\overrightarrow{PR} = \overrightarrow{PQ} + \overrightarrow{QR}$

Step2: Substitute given vectors

$\overrightarrow{PR} =

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

+

$$\begin{pmatrix} 4 \\ 1 \end{pmatrix}$$

$

Step3: Add corresponding components

$\overrightarrow{PR} =

$$\begin{pmatrix} 3+4 \\ 2+1 \end{pmatrix}$$

=

$$\begin{pmatrix} 7 \\ 3 \end{pmatrix}$$

$

Answer:

$$\begin{pmatrix} 7 \\ 3 \end{pmatrix}$$