The distance formula in three dimensions is:
distance = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
For a point to lie on the sphere with center (0,0,0) and radius 5, it must satisfy the equation:
distance = sqrt(x^2 + y^2 + z^2) = 5
We can test each of the given points to see if they satisfy this equation:
A) (4,3,1)
distance = sqrt((4-0)^2 + (3-0)^2 + (1-0)^2) = sqrt(16 + 9 + 1) = sqrt(26) ≠ 5
B) (-5,0,0)
distance = sqrt((-5-0)^2 + (0-0)^2 + (0-0)^2) = sqrt(25) = 5
C) (0,-3,4)
distance = sqrt((0-0)^2 + (-3-0)^2 + (4-0)^2) = sqrt(9 + 16) = sqrt(25) = 5
D) (0,0,6)
distance = sqrt((0-0)^2 + (0-0)^2 + (6-0)^2) = sqrt(36) = 6 ≠ 5
Therefore, the points on the sphere are B) (-5,0,0) and C) (0,-3,4).
A sphere has center (0,0,0) and a radius of 5. Which of the following points lies on the sphere? Use the distance formula, but adjust it to be used fir three variables instead of two.
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