Need help finding the angle between curves
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Need help finding the angle between curves

[From: ] [author: ] [Date: 12-08-05] [Hit: ]
r2(1) = [2,r1(1)/|r1(1)| = [1/sqrt(10),r2(1)/|r2(1)| = [2/sqrt(5),a = 45 degrees.......
Using vectors, find the angle between the curves y=x^3 and x=y^2 at the point (1,1).

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Parametrize the curves, find the unit tangent vector of each at (1,1), take the dot product, then take the inverse cosine.
r1 = [t, t^3]
r2 = [t^2, t]

r1' = [1, 3t^2]
r2' = [2t, 1]

r1'(1) = [1, 3]
r2'(1) = [2, 1]

r1'(1)/|r1'(1)| = [1/sqrt(10), 3/sqrt(10)]
r2'(1)/|r2'(1)| = [2/sqrt(5), 1/sqrt(5)]

cos(a) = 5 / sqrt(50) = sqrt(2) / 2
a = 45 degrees.
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