Given that \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix}\) and \(AC = \begin{pmatrix} 2 \\
FURTHER MATHEMATICS
WAEC 2014
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. \(2\sqrt{10}\)
Explanation
\(BC = BA + AC\)
Given, \(AB\), then \(BA = - AB\)
= \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix} \implies BA = \begin{pmatrix} -4 \\ -3 \end{pmatrix}\)
\(\therefore BC = \begin{pmatrix} -4 \\ -3 \end{pmatrix} + \begin{pmatrix} 2 \\ -3 \end{pmatrix}\)
= \(\begin{pmatrix} -2 \\ -6 \end{pmatrix}\)
\(|BC| = \sqrt{(-2)^{2} + (-6)^{2}} = \sqrt{40} \)
= \(2\sqrt{10}\)
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