Question

is this vector field F tangent to or normal to the curve C

Answer 1

F=<y,-x> where C={(x,y):x^2+y^2=1} and n=<x,y>

Answer 2

n is a normal to C

Answer 3

i think is tangent but i'm not sure

Answer 4

Take the dot product of the normal vector and F:
\[<y, -x>*<x,y>=xy-xy=0\]Since the vectors are orthogonal, the vector field cannot be normal to the curve (if it was, F and n would be parallel). Since your only other choice is parallel, they are parallel.

Answer 5

I mean tangent...lol

Answer 6

so its normal at all points to C?

Answer 7

Another way to see this is to note that C is just a unit circle:No, F is tangent to all point of C

Answer 8

yea C is only circle and the vector F goes in circles so that means its tangent at all points on C?

Answer 9

F is tangent because it is orthogonal to the normal vector n.