Doubt from vector

The angular bisector of \vec{a} , \vec{b} in this case will be of the form \lambda(\vec{a} + \vec{b}).

So any vector of the form \lambda(\vec{a} + \vec{b})+\mu (\vec{a} \times \vec{b}) will be equally inclined to both given vectors

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Can you explain this how?

Can anyone explain why this happens?

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I think this is the perfect answer.
Rest all ANSWERS are a part of this family of vectors [k(A + B) + h(A x B)].

Vectors are represented in Strong Text
Let C be the Angular Bisector of A and B
C = k {{[ A / |A| ] + [ B / |B| ]}}
Now as we know, Cross Pdt of any two vectors gives us a vector perpendicular to both of them.
Let D = h{[A x B]}
Now all the vectors lying in the plane (defined by the two vectors i.e. C & D) are equally inclined to A & B.
And any vector in that plane can be represented as {xC+yD}.
Hence...