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

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Aicharya · Accepted Answer

c &#8594; = x a &#8594; + y b &#8594; + a &#8594; &#215; b &#8594; c &#8594; . a &#8594; = x &#160; a n d &#160; x = 2 cos &#8289; &#945; c &#8594; . b &#8594; = y &#160; a n d &#160; y = 2 cos &#8289; &#945; Also, a &#8594; &#215; b &#8594; = 1 &#8756; &#160; &#160; c &#8594; = 2 cos &#945; &#8289; a &#8594; + b &#8594; + a &#8594; &#160; &#215; b &#8594; c &#8594; 2 = 4 cos 2 &#8289; &#945; a &#8594; + b &#8594; 2 + a &#8594; &#215; b &#8594; 2 + 4 cos &#8289; &#945; a &#8594; + b &#8594; . a &#8594; &#215; b &#8594; 4 = 8 cos 2 &#8289; &#945; + 1 8 cos 2 &#8289; &#945; = 3

Let a → and b → be two unit vectors such that a → . b → = 0 . For some x , y ∈ R, let c → = x a → + y b → +…

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