# 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

Can you explain this how?

Can anyone explain why this happens?

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 {

*x*}.

**C**+y**D**Hence...