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The vector  lies in the plane of the vector  and  and bisects the angle between  and . Then, which one of the following gives possible values of α and β ?

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  1. α = 2, β = 2
  2. α = 1, β = 2
  3. α = 2, β = 1
  4. α = 1, β = 1

Answer (Detailed Solution Below)

Option 4 : α = 1, β = 1
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Detailed Solution

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Concept: 

If two or more vectors lie on the same plane than they are called coplanar vector and satisfies the conditions .

Calculation: 

Also,  bisects the angle between  and .

On comparing with  ,

We get, λ = √ 2, α =1, and β = 1

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