If (1,-1,2) and (2,1,-1) are the end points of a diameter of a sphere x^2+y^2+z^2+2 u x+2 v y+2 w z-1=0 , then what is u+v+w equal to?

Step-by-step solution

The general equation x^2+y^2+z^2+2 u x+2 v y+2 w z+d=0 represents a sphere with centre (-u,-v,-w) and radius r= u^2+v^2+w^2-d If B is the mid point of the line segment A C where A = (x₁, y₁, z₁ ) and C = (x₂, y₂, z₂ ) then. B = ( x₁+x₂ 2 , y₁+y₂ 2 , z₁+z₂ 2 ) Given, equation of sphere x^2+y^2+z^2+2 u x+2 v y+2 w z-1=0 with AB as its diameter and A =(1,-1,2) and B =(2,1,-1) aligned C & = ( 1+2 2 , 1-1 2 , -1+2 2 ) & = ( 3 2 , 0, 1 2 ) aligned We know that centre of the sphere is given by (-u,-v,-w) Comparing, then w