Find the equation of the sphere which passes through `(1,0,0),(0,1,0)` and `(0,0,1)` and whose centre lies on the plane `3x-y+z=2.`

Explanation

To find the equation of the sphere that passes through the points (1, 0, 0), (0, 1, 0), and (0, 0, 1), and whose center lies on the plane \(3x - y + z = 2\), we will follow these steps:

### Step 1: General Equation of the Sphere
The general equation of a sphere can be expressed as:
\[ x^2 + y^2 + z^2 + 2ux + 2vy + 2wz + d = 0 \]
where \((-u, -v, -w)\) is the center of the sphere.
...