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°
Correct Answer: Option C
Explanation
(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°)