- #1
B.Cantarelli
- 4
- 0
Question:
What are the vector, parametric and symmetric equations of the angle bissector of angle ∠ABC, given that A=(1,2,3), B=(3,4,5) and C=(6,7,0).
Attempt at resolution:
Well, I defined some D=(d_1,d_2,d_3) to be a point in the angle bissector, and two lines r:X=(3+2a,4+2a,5+2a) and s:Y=(3+3b,4+3b,5-5b) for any a,b, which are the lines defined by points A and B and B and C respectively.
So, I realize that the distance between D and r must be the same as the distance between D and s, and that D=(d_1,d_2,d_3)=(3-2m+3n,4-2m+3n,5-2m-5n) for some m and n. The problem is that I do not seem to be able to find some efficient way to solve for these restrictions.
What are the vector, parametric and symmetric equations of the angle bissector of angle ∠ABC, given that A=(1,2,3), B=(3,4,5) and C=(6,7,0).
Attempt at resolution:
Well, I defined some D=(d_1,d_2,d_3) to be a point in the angle bissector, and two lines r:X=(3+2a,4+2a,5+2a) and s:Y=(3+3b,4+3b,5-5b) for any a,b, which are the lines defined by points A and B and B and C respectively.
So, I realize that the distance between D and r must be the same as the distance between D and s, and that D=(d_1,d_2,d_3)=(3-2m+3n,4-2m+3n,5-2m-5n) for some m and n. The problem is that I do not seem to be able to find some efficient way to solve for these restrictions.
Last edited: