Respuesta :
Answer:
a) r*dr/dt = 0 (dot product)
b) this argument can be generalized even to 3D
Step-by-step explanation:
for a circular path the relationship between x and y is
x²+y² = R² , where R= radius of the circle
for any point (x,y) the position vector is r and the velocity is the change in position with time , therefore v= dr/dt
if we do the dot product of r and itself
r * r = (x,y)*(x,y) = x² + y² = R² ( constant)
r * r = R²
taking the derivative of r with respect to the time t
r * dr/dt + dr/dt * r = d(R²)/dt
2*r*dr/dt = 0
r*dr/dt = 0
therefore
r*dr/dt = 0
since the dot product of r and dr/dt is 0 they are orthogonal to each other.
For 3D , the equation of a sphere is
x²+y²+z³= R²
following the same steps than before we get r * r = (x,y,z)*(x,y,z) = x² + y² +z² = R²
and thus also r*dr/dt = 0
then this argument can be generalized even to 3D
