There are two vectors called $\vec{a}$ and $\vec{b}$. Vector $\vec{c}$ is the bisector and it can be given as
$$\vec{c} = |b|\vec{a} + |a|\vec{b}$$
How to prove that? I have used the dot product method. But there I can't find the angle between them. Then I tried to do this by using unit vectors. Then I got an answer like in the given picture. The answer which I got. Can you help me to get the correct answer
Best Answer
Here's a purely geometric argument.
By definition, the sum of two vectors is equal to the diagonal of the parallelogram spanned by the vectors.
Now, observe that the two vectors $|b|\vec{a}$ and $|a|\vec{b}$ have exactly the same length. Therefore the parallelogram they span is a rhombus. The result then follows from the fact that the diagonal of a rhombus bisects its angles.