I do not really follow the question!
However, I can give you the expression for the bisector be the two vectors.
.
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
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.
The answer = {-2,10,8}
The 2nd answer = {2,-10,-8}
please explain for me, how to solve it! step by step. Thanks in advance
Thank you in advance
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
this leads to
k^2+25k^2+16k^2=42 x 4
k^2=4
k=2 or k=-2
And thus the answer.
Civodul