Homework Help: Find a vector c that bisects the angle

1. Apr 8, 2005

particleaccelerater

any help is appreciated

Find a vector c that bisects the angle between the vectors a = i + 5j - 2k andb = -3i + j + 6k.

2. Apr 8, 2005

jdavel

particle,

Could you find one if a and b had the same magnitude?

3. Apr 8, 2005

particleaccelerater

no i have never done anything like this but i can descirbe the scenario to you

this is for program iam writing for a laser beam. two arbitrary vectors represent the two distances from the laser to the mirror and from the mirror to a target. The bisector represents the normal of the plane(really the mirror). From that bisector, i will have to find the angles the mirror is being pivoted and rotated.

( i would much rather you demonstrate it on this example, i can understand it better by seeing the math, but not visually in my head) thx for any help you can give me

4. Apr 8, 2005

jdavel

particle,

"i would much rather you demonstrate it on this example, i can understand it better by seeing the math, but not visually in my head"

I'll get to this example when you're ready for it!

From a single point, draw two different vectors with equal magnitudes. Now draw their sum. Does that help?

5. Apr 8, 2005

particleaccelerater

i can add vectors in 2d ut not 3d

6. Apr 8, 2005

chroot

Staff Emeritus
It's precisely the same thing, particleaccelerator. Put the vectors tail-to-head and draw the resultant line. Or, analytically, just add the components.

- Warren

7. Apr 8, 2005

particleaccelerater

is it -2i + 6j + 4k? just add the components?

8. Apr 8, 2005

The Bob

Yeap. That is the sum of the two vectors.

The Bob (2004 ©)

9. Apr 8, 2005

particleaccelerater

will someone just do this example for me so ican understand it, icant see it visually very well

10. Apr 8, 2005

particleaccelerater

so the sum of two vectors is the bisector of the angle between the vectors?

11. Apr 8, 2005

The Bob

Might be. Let me think in 3D first.

The Bob (2004 ©)

12. Apr 8, 2005

The Bob

I believe it would give you the direction of the bisector.

The Bob (2004 ©)

13. Apr 8, 2005

particleaccelerater

assuming a plane to be a mirror and two vectors coming from the same point on the plane where the point represents the point of reflection on the mirror, does the resultant of these two vectors represent the normal of the plane(mirror). i am trying to figure this out becuase given the coordinates of where the target should be, i have to pivot the mirror horizantally and vertically to make this happen

14. Apr 8, 2005

jdavel

particle,

You said you can add vectors in 2d. Try it with 2 vectors of equal magnitude (length) and then with two vectors of different magnitude. See if that answers your question:"so the sum of two vectors is the bisector of the angle between the vectors?"

15. Apr 8, 2005

particleaccelerater

assuming a plane to be a mirror and two vectors coming from the same point on the plane where the point represents the point of reflection on the mirror, does the resultant of these two vectors represent the normal of the plane(mirror). i am trying to figure this out becuase given the coordinates of where the target should be, i have to pivot the mirror horizantally and vertically to make this happen

16. Apr 8, 2005

jdavel

particle,

Ok, I give up! You don't want to learn anything; you just want somebody to do your work for you. If you wait around long enough somebody probably will. But it won't be me.

Good luck!

17. Apr 8, 2005

particleaccelerater

all i want is for somebody to tell me if my thinking is right

assuming a plane to be a mirror and two vectors coming from the same point on the plane where the point represents the point of reflection on the mirror, does the resultant of these two vectors represent the normal of the plane(mirror)??????

i am trying to figure this out becuase given the coordinates of where the target should be, i have to pivot the mirror horizantally and vertically to make this happen

18. Apr 9, 2005

The Bob

I empathsis with jdavel but I am going to see what I can do for particles understanding.

First off, http://descartes.cnice.mecd.es/ingles/Bach_CNST_1/Analytical_geometry/Geometria_8-1.htm [Broken] might help.

See if that helps. I need to think of a way of describing what you need to do.

The Bob (2004 ©)

Last edited by a moderator: May 2, 2017
19. Apr 9, 2005

The Bob

Right. I have had a think and here is what I have come up with. This example is in 2D.

Find two points at the end of the vectors in the same way you use co-ordinate for normal equations of y and x.

Use this points to find the mid-point of the line that would join them e.g:

$$(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2})$$

Then use this and the origin to find the equation of the line with the second general equation e.g. y1 - y2 = m(x1 - x2).

See if it can be applied to 3D and you are away.

The Bob (2004 ©)