Answer :

Given :


Let, A, B, C & D be four points with given position vectors






To Find : value of λ


Formulae :


1) Vectors :


If A & B are two points with position vectors ,


Where,




then vector is given by,




2) Scalar Triple Product:


If





Then,



3) Determinant :



Answer :


For given position vectors,






Vectors are given by,




………eq(1)




………eq(2)




………eq(3)


Now, for vectors







= -2(- λ – 10) – 3(13) + 1(28 – 5λ)


= 2λ + 20 – 39 + 28 – 5λ


= 9 – 3λ


………eq(4)


Four points A, B, C & D are coplanar if and only if


………eq(5)


From eq(4) and eq(5)


9 – 3λ = 0


3λ = 9



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