The correct option is C 1
Let the four points be P, Q, R, S respectively. The
−−→PQ=4^i+6^j+(λ+1)^k,−−→QR=−^i+4^j+(4−λ)^k,−−→RS=−7^i−5^j+0^k,
The given points are coplanar, therefore −−→PQ,−−→QR,−−→RS are coplanar and so [−−→PQ,−−→QR,−−→RS]=0
⇒∣∣
∣∣46λ+1−144−λ−7−50∣∣
∣∣=0⇒λ=1