Find the value of `lambda` for which the four points with position vectors `- hat j- hat k ,4 hat i+5 hat j+lambda hat k ,3 hat i+9 hat j+4 hat k` and `4 hat i+4 hat j+4 hat k` are coplanar.

Explanation

Let `vecA = -hatj-hatk`

`vecB = 4hati+5hatj+lambda hat k`

`vecC = 3hati+9hatj+4 hat k`

`vecD = -4hati+4hatj+4hat k`

Now, `vec(AB) = vecB - vecA = 4hati+6hatj+(lambda+1) hat k`

`vec(AC) = 3hati+10hatj+5hat k`

`vec(AD) = -4hati+5hatj+5hat k`

If all these three vectors are coplanar then their triple product will be `0`.

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