Questions
A vector lies in the plane of the vectors and . If bisects the angle between and, . then
detailed solution
Correct option is D
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=0Similar Questions
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