# Show that Vector function lies on a sphere

1. May 16, 2010

### karens

1. The problem statement, all variables and given/known data

Let r1 and r2 be differentiable 3-space vector-valued functions.

Show that for a differentiable 3-space vector-valued function r, the graph of r lies on a sphere centered at the origin if and only if r(t) and r′(t) are orthogonal (perpendicular) for all t.

2. Relevant equations

Dot products?

3. The attempt at a solution
If R(t) is on the surface of such a sphere then ||R(t)||=C, is constant.

2. May 16, 2010

### lanedance

so, if i;m interpreting this correctly if ||r(t)||=c, then you could write it as:

$$\textbf{r}(t) \bullet \textbf{r}(t) = c^2$$