If the vectors m i +m j +n k , i + k , n i +n j +p k lie in a plane then...

MHT CET 2025 Mathematics question

If the vectors lie in a plane then...

(A)m+n+p=0
(B)m,n,p are in A.P.
(C)m,n,p are in G.P.Correct
(D)n,m,p are in G.P.

Answer: (C)

Solution

Three vectors lie in one plane (are coplanar) exactly when their scalar triple product is zero: . Expanding along the first row: $m(0· p-1· n)-m(1· p-1· n)+n(1·

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Question ID VK-102261