A vector  a→=αi^+2j^+βk^, α,β∈R lies in the plane of the vectors b→=i^+j^ and c→=i^−j^+4k^. If a→bisects the angle between b→ andc→, . then

Angle bisector can be  a→=λb^+c^  or   a→=μb^−c^Now a→=λi^+j^2+i^-j^+4k^32=λ323i^+3j^+i^−j^+4k^=λ324i^+2j^+4k^          Comparing  with a→=αi^+2j^+βk^ we get                                               2λ32=2⇒λ=32          ⇒a→=4i^+2j^+4k^                   None of the option is satisfied. So, now considera→=μi^+j^2−i^−j^+4k^32      ⇒a→=μ323i^+3j^−i^+j^−4k^               =μ322i^+4j^−4k^                               Comparing witha→=αi^+2j^+βk^, we get    4μ32=2⇒μ=322⇒a→=i^+2j^−2k^Now a→.k^+2=-2+2=0