Find `lambda` for which the points `A(3,\ 2,\ 1),\ B(4,\ lambda,\ 5),\ C(4,\ 2,\ -2)\ a n d\ D(6,\ 5,\ -1)` are coplanar.

Explanation

`vecAB = vecB-vecA=hati+(lambda-2)hatj+4hatk`

`vecAC = vecC-vecA=hati+0hatj-3hatk`

`vecAD = vecD-vecA=3hati+3hatj-2hatk`

Since, `A,B,C,D` are coplanar, thus

`[[vecAB,vecAC,vecAD]]=0`

`|[1,(lambda-2),4],[1,0,-3],[3,3,-2]|=0`

`1(0+9)-(lambda-2)(-2+9)+4(3-0)=0`

`7lambda-35=0`

...