How do you find the angle between the vectors #u=3i+4j# and #v=-2j#?

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Answer 1 · 2016-12-20T07:43:29

The answer is #=143.1º#

The angle between 2 vectors is given by the dot product

#vecu.vecv=∥vecu∥*∥vecv∥ costheta#

Here,

#vecu=〈3,4〉#

#vecv=〈0,-2〉#

The dot product is #vecu.vecv=〈3,4〉.〈0,-2〉=0-8=-8#

The modulus of #vecu# is #=∥〈3,4〉∥=sqrt(9+16)=sqrt25=5#

The modulus of #vecv# is #=∥〈0,-2〉∥=sqrt(4)=2#

The angle is

#costheta=(vecu.vecv)/(||vecu||*||vecv||)#

#=-8/(5*2)=-0.8#

#theta=143.1º#