anonymous
  • anonymous
Find the points on the sphere x² +y² +z²= 36 that are closest to and farthest from the point (1,2,2).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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experimentX
  • experimentX
let's see .. let x1,y1,z1 be the points on sphere for the points to be closest, 1,2,2 must line in the radius connecting x1,y1,z1 so, x1/sqrt(x1^2+y1^2+z1^2) = 1/sqrt(1^2+2^2+2^2) y1/sqrt(x1^2+y1^2+z1^2) = 2/sqrt(1^2+2^2+2^2) z1/sqrt(x1^2+y1^2+z1^2) = 2/sqrt(1^2+2^2+2^2) as we know, r = 6, we have sqrt(x1^2+y1^2+z1^2) = 6 x/6 = 1/sqrt(1^2+2^2+2^2); y/6 = 2/sqrt(1^2+2^2+2^2); z/6 = 2/sqrt(1^2+2^2+2^2) must give the closest point. so your answer must be http://www.wolframalpha.com/input/?i=x%2F6+%3D+1%2Fsqrt%281%5E2%2B2%5E2%2B2%5E2%29%3B+y%2F6+%3D+2%2Fsqrt%281%5E2%2B2%5E2%2B2%5E2%29%3B+z%2F6+%3D+2%2Fsqrt%281%5E2%2B2%5E2%2B2%5E2%29 for the farthest point, we have the other point on the other side of the sphere (-x,-y,-z) for the same values

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