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The shortest distance from the point (1, 2, -1) to the surface of the sphere x2 + y2 + z2 = 24 is
  • a)
    3√6
  • b)
    2√6
  • c)
    √6
  • d)
    2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The shortest distance from the point (1, 2, -1) to the surface of the ...
Distance from a Point to a Surface of a Sphere
To find the shortest distance from a point to the surface of a sphere, we need to first calculate the distance between the point and the center of the sphere and then subtract the radius of the sphere.

Given Information
Point: (1, 2, -1)
Sphere: x^2 + y^2 + z^2 = 24

Calculations
1. Find the center of the sphere:
The center of the sphere is at the origin since the equation of the sphere is x^2 + y^2 + z^2 = r^2, where (0, 0, 0) is the center.
2. Calculate the distance between the point and the center of the sphere:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Distance = sqrt((0 - 1)^2 + (0 - 2)^2 + (0 - (-1))^2)
Distance = sqrt(1 + 4 + 1)
Distance = sqrt(6)
3. Subtract the radius of the sphere:
Radius of the sphere = sqrt(24) = 2sqrt(6)
Shortest distance = Distance - Radius = sqrt(6) - 2sqrt(6) = -sqrt(6)

Conclusion
The shortest distance from the point (1, 2, -1) to the surface of the sphere x^2 + y^2 + z^2 = 24 is sqrt(6). Therefore, the correct answer is option 'a'.
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The shortest distance from the point (1, 2, -1) to the surface of the sphere x2 + y2 + z2 = 24 isa)3√6b)2√6c)√6d)2Correct answer is option 'C'. Can you explain this answer?
Question Description
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