The smallest radius of the sphere passing through the points `(1,0,0), (0, 1,0) and (0,0,1)` is equal to `sqrt(2/3)`.

Answer

To prove that the smallest radius of the sphere passing through the points \( (1,0,0) \), \( (0,1,0) \), and \( (0,0,1) \) is equal to \( \sqrt{\frac{2}{3}} \), we will follow these steps:

### Step 1: Write the equation of the sphere
The general equation of a sphere in three-dimensional space is given by:
\[ x^2 + y^2 + z^2 + 2ux + 2vy + 2wz + d = 0 \]
where \( (u, v, w) \) are the coordinates of the center of the sphere and \( d \) is a constant.