Angle between vectors

Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)

Result

A =  0 °

Solution:

u=(22)2+112=11 524.5967 v=162+202=4 4125.6125 s=(22) (16)+(11) (20)=132 A=180πarccos(s/(u v))=180πarccos((132)/(24.5967 25.6125))102.09480u=\sqrt{ (-22)^{ 2 }+11^{ 2 } }=11 \ \sqrt{ 5 } \doteq 24.5967 \ \\ v=\sqrt{ 16^{ 2 }+20^{ 2 } }=4 \ \sqrt{ 41 } \doteq 25.6125 \ \\ s=(-22) \cdot \ (16)+(11) \cdot \ (20)=-132 \ \\ A=\dfrac{ 180^\circ }{ \pi } \cdot \arccos(s/(u \cdot \ v))=\dfrac{ 180^\circ }{ \pi } \cdot \arccos((-132)/(24.5967 \cdot \ 25.6125)) \doteq 102.0948 \doteq 0 ^\circ



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