How to determine the cosine of the angle between the vectors u and v? u=3i-4j v=2i+j

Expert Answers

We have the vectors u = 3i - 4j and v = 2i + j.

Now the cosine of the angle between two vectors A = a1*i + b1*j and B = a2*i + b2*j is given by

cos theta=(a1*b1+a2*b2)/[sqrt(a1^2+b1^2)*sqrt(a2^2+b2^2)

=> cos theta = (3*2 - 4*1)/ sqrt (9 + 16)* sqrt (4 +1)

=> cos theta = (6 - 4)/ 5*sqrt 5

=> cos theta = 2 / 5 sqrt 5

=> cos theta = 2*sqrt 5 / 25

Therefore the required cosine of the angle between u = 3i - 4j and v = 2i + j is 2*sqrt 5 / 25

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