1. Let F = -yi + xj and let C be the unit circle oriented counterclockwise. (a) Show that F has constant magnitude on C. (b) Show that F is always tangent to the circle C. (c) Show that S¢F•dr = length of C.

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1. Let F = -yi + xj and let C be the unit circle oriented counterclockwise.
(a) Show that F has constant magnitude on C.
(b) Show that F is always tangent to the circle C.
(c) Show that SoF·dr = length of C.
Transcribed Image Text:1. Let F = -yi + xj and let C be the unit circle oriented counterclockwise. (a) Show that F has constant magnitude on C. (b) Show that F is always tangent to the circle C. (c) Show that SoF·dr = length of C.
Expert Solution
Step 1

a.)

Let us parametrize C.

Since it's a circle of radius 1,

r(t)=<cos t, sin t> where 0t2π

and so

F(r(t))=<-sin(t), cos (t)> =sin2(t)+cos2(t)=1=1

 

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