If the position vectors (-jcap-kcap), (4icap+5jcap+lambdakcap), (3icap+9jcap+4kcap) and (-4icap+4jcap+4kcap)are coplanar, than the value of lambda is
1. -1
2. 0
3. 1
4. 2

please give your choice with explanation
please specify that what is the condition of coplanar...

A=(0,-1,-1), \;\ B=(4,5,L), \;\ C=(3,9,4), \;\ D=(-4,4,4)

AB=-4i-6k+(-L-1)k

AC=-3i-10j-5k

AD=4i-5j-5k

Cross Product:

AC\times AD=25i-35j+55k

Dot product of ACxAD and AB

\begin{vmatrix}25&-35&55\\-4&-6&-L-1\end{vmatrix}=55-55L

The dot product is 0 if they are coplanar.

55-55L=0\Rightarrow L=1

Thanks a lot for your answer