If the volume of parallelepiped formed by the vectors i ^ + λ j ^ + k ^ , j ^ + λ k ^ and λ i ^ + k ^ is minimum, then λ is equal to:

Question

If the volume of parallelepiped formed by the vectors i ^ + λ j ^ + k ^ , j ^ + λ k ^ and λ i ^ + k ^ is minimum, then λ is equal to:, - 1 3, - 3, 3, 1 3

MARKS App · Accepted Answer

Volume of parallelopiped = A → B → C → Let f ( λ ) = 1 λ 1 0 1 λ λ 0 1 = λ 3 - λ + 1 f ' ( λ ) = 3 λ 2 - 1 = 3 λ + 1 3 λ - 1 sign conversion for f ' λ at λ = 1 3 , f ' λ changes its sign from - ve to + ve ∴ λ = 1 3 , is the point of minima. ⇒ At λ = 1 3 volume of parallelopiped is minimum.

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