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Paragraph: Let A(1,-1,2) and B(2,1,-1) be the end points of the diameter of the sphere x^2+y^2+z^2+2 u x+2 v y+2 w z-1=0 Question: If P(x, y, z) is any point on the sphere, then what is P A^2+P B^2 equal to?

Options

  1. A15
  2. B14
  3. C13
  4. D6.5

Correct answer

B. 14

Step-by-step solution

A P B=90^ P A^2+P B^2=A B^2=(2-1)^2+(1+1)^2+(-1-2)^2=1+4+9=14

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