# Math Help - Vector problem (solved but I need explanation)

1. ## Vector problem (solved but I need explanation)

its given

a(vector) = {2; -3; 6}
b(vector) = {-1; 2;-2}

There is an orange line which halfs the angle between two vectors {shown in picture}

Now problem says:
Find a vector over orange line {showed in the picture} that length is $2 \sqrt(42)$

note! The problem doesnt say that vectors starts from {0,0,0} point, I just draw the figure to illustrate it more better. The problem doesn't contain any picture with it.

please explain for me, how to solve it! step by step. Thanks in advance

2. I do not really follow the question!
However, I can give you the expression for the bisector be the two vectors.
$\left\| b \right\|a + \left\| a \right\|b$.

3. The orange line is the bisector of vectors a and b and as plato wrote one vector that directs this line is:

(if this is not clear say so)

In our case this leads to a vector c which coordinates are

c (-1; 5; 4)

Now any vector colinerar to c "will be" on the orange line, so will have coordinates (-k; 5k; 4k)

now we want the norm of this vector to be