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Find the radius of the sphere represented by x² + y² + z² = 49 and the plane 2x + 3y - z - 5√14 = 0.

1. √6
2. 2√6
3. 4√6
4. 6√6

Correct answer: 2√6

Solution

The equation of the sphere indicates that its radius is the square root of 49, which is 7. The distance from the center of the sphere to the plane is calculated using the formula for the distance from a point to a plane, and this distance is found to be 2√6. Therefore, the radius of the sphere that intersects with the plane is 2√6.

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