Given that \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix}\) and \(AC = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\), find |BC|.
A. \(4\sqrt{2}\)
B. \(6\sqrt{2}\)
C. \(2\sqrt{10}\)
D. \(4\sqrt{10}\)
Correct Answer: C
Explanation
\(BC = BA + AC\)
Given, \(AB\), then \(BA = - AB\)
= \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix} \implies BA = \begin{pmatrix} -4 \\ -3 \end{pmatrix}\)
\(\therefore BC = \begin{pmatrix} -4 \\ -3 \end{pmatrix} + \begin{pmatrix} 2 \\ -3 \end{pmatrix}\)
= \(\begin{pmatrix} -2 \\ -6 \end{pmatrix}\)
\(|BC| = \sqrt{(-2)^{2} + (-6)^{2}} = \sqrt{40} \)
= \(2\sqrt{10}\)
