D ABC is a tetrahedron with A=(2,0,0),B=(0,4,0) and CD=14. Edge CD lies  on the line x−11=y−22=z−33. If locus of centroid of tetrahedron is x−321=y−y1a=z−z1b, then which of the following is/are true:

Let C=λ1+1,2λ1+2,3λ1+3 and D=λ2+1,2λ2+2,3λ2+3∴CD=14λ1−λ2=14⇒λ1=λ2+1⇒  Let centroid (α,β,γ)=5+2λ24,10+4λ24,9+6λ24∴ Locus is 4x−52=4y−104=4z−96∴ Dr's of line 1,2,3 and point 32,3,3 satisfies the line ∴ locus is x−321=y−33=z−33