Given: and are coplanar.

Also given that, and are coplanar.

Now, using the condition of coplanar we get,

Expanding the determinant along R 1 .

(b-1)-(1-c)+a(1-bc)=0

a + b + c = 2 + abc .....(i)

Again using the coplanar condition we get,

Apply row transformations,

Expand the determinant along R 1 .

(a + b)(0 + 2ac)-c(0 + 2a 2 )+c(-2ac + 2a(b + c))= 0

2a 2 c + 2abc - 2a 2 c - 2ac 2 + 2abc + 2ac 2 = 0

abc = 0

a + b + c = 2 (From eq (i))

6(a + b + c)= 12

Hence this is the correct option.

──────────────────────────────────────────────────────────────────────────────────────────