Position vector perpendicular to tangent vector yields a sphere

[physicsidiot1]

Homework Statement

If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t), show that the curve lies on a sphere with center the origin.

Homework Equations

-1/r'(t)= slope of position vector

x$$^{2}$$+y$$^{2}$$=1

The Attempt at a Solution

Not really sure where to begin for this one.

 

[tiny-tim]

hi physicsidiot1!

… the position vector r(t) is always perpendicular to the tangent vector r'(t) … the curve lies on a sphere with center the origin.

this is a vector problem, so it needs a vector solution

start by writing the question out in two vector equations …

what do you get? ​