Given that \(r = 3i + 4j\) and \(t = -5i + 12j\), find the acute angle between them.

  • A 14.3°
  • B 55.9°
  • C 59.5°
  • D 75.6°
waec 2016furthermathematics

The correct answer is C. 59.5°

\(\overrightarrow{r} . \overrightarrow{t} = |\overrightarrow{r}||\overrightarrow{t}|\cos \theta\)

\(\overrightarrow{r} . \overrightarrow{t} = (3i + 4j) . (-5i + 12j) = -15 + 48 = 33\)

\(|\overrightarrow{r}| = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5\)

\(|\overrightarrow{t}| = \sqrt{(-5)^{2} + 12^{2}| = \sqrt{169} = 13\)

\(\cos \theta = \frac{\overrightarrow{r} . \overrightarrow{t}}{|\overrightarrow{r}||\overrightarrow{t}|}\)

 \(\cos \theta = \frac{33}{5 \times 13} = \frac{33}{65}\)

\(\theta = \cos^{-1} {\frac{33}{65}} \approxeq 59.5°\)

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