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: C
Explanation
\(PQ = \begin{pmatrix} 7 - 3 \\ 4 - 1 \end{pmatrix}\)
\(= \begin{pmatrix} 4 \\ 3 \end{pmatrix}\)
\(\hat{n} = \frac{\overrightarrow{PQ}}{|PQ|} \)
\(|PQ| = \sqrt{4^{2} + 3^{2}} = \sqrt{25} = 5\)
\(\hat{n} = \frac{1}{5}\begin{pmatrix} 4 \\ 3 \end{pmatrix} = \begin{pmatrix} 0.8 \\ 0.6 \end{pmatrix}\)
