On which one of the following planes does the centre of S lie?
For the following two (02) items: Suppose S is the sphere with the <strong>SMALLEST</strong> radius that passes through the points A(1,0,0), B(0,1,0) and C(0,0,1).
- A. x+y+z-1=0 ✓
- B. x+y+z+1=0
- C. 3x+3y+3z-1=0
- D. 3x+3y+3z+1=0
Correct Answer: A. x+y+z-1=0
Explanation
From the previous calculation, the center of the sphere is (1/3, 1/3, 1/3). Substituting these coordinates into the given plane equations, only x+y+z-1=0 evaluates to true: 1/3 + 1/3 + 1/3 - 1 = 1 - 1 = 0.
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