Let a → and b → be two unit vectors such that a → . b → = 0 . For some x , y ∈ R, let c → = x a → + y b → + a → × b → . If c → = 2 and the vector c → is inclined at the same angle α to both a → and b → , then the value of 8 cos 2 α is

Question

Let a → and b → be two unit vectors such that a → . b → = 0 . For some x , y ∈ R, let c → = x a → + y b → + a → × b → . If c → = 2 and the vector c → is inclined at the same angle α to both a → and b → , then the value of 8 cos 2 α is,

MARKS App · Accepted Answer

c → = x a → + y b → + a → × b → c → . a → = x a n d x = 2 cos ⁡ α c → . b → = y a n d y = 2 cos ⁡ α Also, a → × b → = 1 ∴ c → = 2 cos α ⁡ a → + b → + a → × b → c → 2 = 4 cos 2 ⁡ α a → + b → 2 + a → × b → 2 + 4 cos ⁡ α a → + b → . a → × b → 4 = 8 cos 2 ⁡ α + 1 8 cos 2 ⁡ α = 3

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