Find for which the points A(3, 2, 1), B(4, λ, 5), C(4, 2, – 2) and D(6, 5, – 1) are coplanar.

Formula: -

and then,

let position vector of

position vector of

position vector of

position vector of

The four points are coplanar if the vector are coplanar

now, using

⇒ 1(9) – (λ – 2)( – 2 + 9) + 4(3 – 0) = 0

⇒ 7λ = 35

⇒ λ = 5