Correct Answer - B
Since a,b,c and u,v ware the vertice of two triangles
Also `c=(1-r) a+ rb `
and `w= (1-r ) u+rb `
Applying `R_3rarr R_3-{(1-r)R_1+rR_2)}`s
`=|{:(" "a" "u" "1),(" "b" "v" "1),(c-(1-r)a-rb w-(1-r)u-rv 1 - (1-r)-r):}|`
`=|(a,u,1),(b,v,1),(0,0,0)|=0 " "[from Eq. (i) ]`