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Given that r=3i+4j and t=5i+12j, find the a...

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 is C

r.t=|r||t|cosθ

r.t=(3i+4j).(5i+12j)=15+48=33

|r|=32+42=25=5

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

cosθ=r.t|r||t|

 cosθ=335×13=3365

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