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 is C

\(BC = BA + AC\)

Given, \(AB\), then \(BA = - AB\)

= \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix} \implies BA = \begin{pmatrix} -4 \\ -3 \end{pmatrix}\)

\(\therefore BC = \begin{pmatrix} -4 \\ -3 \end{pmatrix} + \begin{pmatrix} 2 \\ -3 \end{pmatrix}\)

= \(\begin{pmatrix} -2 \\ -6 \end{pmatrix}\)

\(|BC| = \sqrt{(-2)^{2} + (-6)^{2}} = \sqrt{40} \)

= \(2\sqrt{10}\)