P and Q are the points (3, 1) and (7, 4) respectively. Find the unit vector along PQ.

A.

\(\begin{pmatrix} 4 \\ 3 \end{pmatrix}\)

B.

\(\begin{pmatrix} 0.6 \\ 0.8 \end{pmatrix}\)

C.

\(\begin{pmatrix} 0.8 \\ 0.6 \end{pmatrix}\)

D.

\(\begin{pmatrix} -0.8 \\ 0.6 \end{pmatrix}\)

Correct answer is C

\(PQ = \begin{pmatrix} 7 - 3 \\ 4 - 1 \end{pmatrix}\)

\(= \begin{pmatrix} 4 \\ 3 \end{pmatrix}\)

\(\hat{n} = \frac{\overrightarrow{PQ}}{|PQ|} \)

\(|PQ| = \sqrt{4^{2} + 3^{2}} = \sqrt{25} = 5\)

\(\hat{n} = \frac{1}{5}\begin{pmatrix} 4 \\ 3 \end{pmatrix} = \begin{pmatrix} 0.8 \\ 0.6 \end{pmatrix}\)