Find the radius of the circular section in which the sphere `|vecr|=5` is cut by the plane `vecr*(hati+hatj+hatk)=3sqrt(3)`

Explanation

To find the radius of the circular section in which the sphere \( |\vec{r}| = 5 \) is cut by the plane \( \vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 3\sqrt{3} \), we can follow these steps:

### Step 1: Identify the Sphere and Plane
The equation \( |\vec{r}| = 5 \) represents a sphere with center at the origin (0, 0, 0) and radius 5. The plane is defined by the equation \( \vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 3\sqrt{3} \).

### Step 2: Find the Distance from the Center of the Sphere to the Plane
To find the distance \( OA \) from the center of the sphere (point O) to the plane, we can use the formula for the distance from a point to a plane. The general formula for the distance \( d \) from a point \( (x_0, y_0, z_0) \) to the plane \( Ax + By + Cz + D = 0 \) is given by:

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