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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: What is u+v+w equal to?

Options

  1. A-2
  2. B-1
  3. C1
  4. D2

Correct answer

A. -2

Step-by-step solution

A(1,-1,2), B(2,1,-1) Centre of sphere =(-u,-v,-w) Centre is mid point of A B(-u,-v,-w)= ( 1+2 2 , -1+1 2 , 2-1 2 )= ( 3 2 , 0, 1 2 ) u= -3 2 , v=0, w= -1 2 u+v+w= -3 2 +0- 1 2 =-2

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