The circumcentre of the triangle formed by the points (1,2,3),(3,-1,5),(4,0,-3) is

Step-by-step solution

Let A, B, C be the vertices of the triangle given as, A (1,2,3), B (3,-1,5), C (4,0,-3) Now, let O(x, y, z) be the circumcentre of A B C . aligned & O A=O B=O C & O A=O B O A^2=O B^2 & aligned (x-1)^2+(y-2)^2+(z-3)^2 =(x-3)^2+(y+1)^2+(z-5)^2 aligned & x^2-2 x+1+y^2-4 y+4+z^2-6 z+9 & =x^2-6 x+9+y^2+2 y+1+z^2-10 z+25 aligned Similarly, O B=O C aligned & (x-3)^2+(y+1)^2+(z-5)^2 & =(x-4)^2+(y-0)^2+(z+3)^2 & x^2-6 x+9+y^2+2 y+1+z^2-10 z+25 & =x^2-8 x+16+y^2+z^2+6 z+9 aligned Similarly, O A=O C gathered (x-1)^2+(y-2)^2+(