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: Option 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})