The correct option is C →a.→c=→b.→c
The lines →r=→a+λ(→b×→c) and →r=→b+μ(→c×→a) pass through points →a and →b, respectively and are parallel to vector →b×→c and →c×→a, respectively.
Therefore, they intersect if →a−→b,→b×→c and →c×→a are coplanar and so
(→a−→b).{(→b×→c)×(→c×→a)}=0⇒(→a−→b).([→b→c→a]→c−[→b→c→c]→a)=0⇒((→a−→b).→c)[→b→c→a]=0⇒→a.→c−→b.→c=0⇒→a.→c=→b.→c