Consider a sphere passing through the origin and the points `(2,1,-1),(1,5,-4),(-2,4,-6)`
What is the radius of the sphere

Options

A. `sqrt12`
B. `sqrt14`
C. 12
D. 14

Answer

B

Explanation

Equation of sphere passing through origin is
`x^2+y^2+z^2+2ux+2vy+2wz=0`
which passes through the points (2,1,-1),(1,5,-4) and (-2,4,-6)
`:. 4u+2v-2w=-6 …(i)`
`2u+10v-8w=-42 …(ii)`
`and -4u+8v-12w=-56 …(iii)`
Form eqns (i),(ii) and (iii), we get
`:." Radius of sphere"=sqrt(u^2+v^2+w^2)`
`=sqrt(1+4+9)=sqrt14`