Let a→ and b→ be two unit vectors such that a→.b→=0. For some x,y∈R, let c→=xa→+yb→+a→×b→. If c→=2 and the vector c→ is inclined at the same angle α…

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Let a→ and b→ be two unit vectors such that a→.b→=0. For some x,y∈R, let c→=xa→+yb→+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 8cos^2 α is

MARKS Content Team · Accepted Answer

Correct answer: 3. c→=xa→+yb→+a→×b→ c→.a→=x and x=2cos⁡α c→.b→=y and y=2cos⁡α Also, a→×b→=1 ∴ c→=2cos α ⁡a→+b→+a→^( )×b→ c→^2=4cos^2⁡αa→+b→^2+a→×b→^2+4cos⁡αa→+b→.a→×b→ 4=8cos^2⁡α+1 8cos^2⁡α=3

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