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Let a → be a unit vector coplanar with i ^ - j ^ + 2 k ^ and 2 i ^ - j ^ + k ^ such that a → is perpendicular to i ^ - 2 j ^ + k ^ . If the projection of a → along i ^ - j ^ + 2 k ^ is λ , then the value of 1 λ 2 is equal to

Correct answer

12

Step-by-step solution

Let, α → = i ^ - j ^ + 2 k ^ ,   β → = 2 i ^ - j ^ + k ^ ,   γ → = i ^ - 2 j ^ + k ^ a → = γ → × α → × β → γ → × α → × β → γ → × α → × β → = γ → ⋅ β → α → - γ → ⋅ α → β → = 5 α → - 5 β → = 5 - i ^ + k ^ a → = - i ^ + k ^ 2 Projection of

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