Find the angle between the vectors displaystyle<{1},{3}>{quadtext{and}quad}<-{2},{4}>

facas9 2021-01-02 Answered
Find the angle between the vectors <1,3>and<2,4>
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Expert Answer

Jozlyn
Answered 2021-01-03 Author has 85 answers
Remember that the angle between two vectors u and v is defined by cos(θ)=uv||u||||v||
So lets calculate uv,||u||,and||v||foru=1,3andv=2,4
uv=1,32,4=2+12=10
||u||=12+32=10
||v||=(2)2+42=20
Now plugging these into our equation, we find that
cos(θ)=101020=12
Looking at the unit circle, we see that cos(θ)=12 at 45and315. Because the angle between two vectors must be between 0and180, that means that the angle between vectors u and v is 45
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