# Find a vector c that bisects the angle

• particleaccelerater
In summary, the conversation is discussing finding a vector c that bisects the angle between two given vectors, a and b. The purpose of finding this vector is for a program that involves a laser beam, where the bisector represents the normal of the plane (mirror) and is used to pivot and rotate the mirror to hit a target. The conversation also discusses adding vectors in 2D and 3D, and whether the sum of two vectors represents the bisector of the angle between them. The conversation ends with a suggestion to use co-ordinates and equations to find the mid-point of the line joining the two vectors in order to find the bisector in 2D and possibly in 3D.
particleaccelerater
any help is appreciated

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

particle,

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

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) thanks for any help you can give me

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?

i can add vectors in 2d ut not 3d

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

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

particleaccelerater said:
is it -2i + 6j + 4k? just add the components?
Yeap. That is the sum of the two vectors.

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

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

particleaccelerater said:
so the sum of two vectors is the bisector of the angle between the vectors?
Might be. Let me think in 3D first.

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

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

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?"

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

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!

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

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 might help.

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

Last edited by a moderator:
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.

## 1. What is a vector c that bisects the angle?

A vector c that bisects an angle is a vector that divides the angle into two equal parts.

## 2. How do I find a vector c that bisects the angle?

To find a vector c that bisects an angle, you can use the following formula:
c = (a + b) / 2
where a and b are two vectors that form the angle.

## 3. Can a vector c bisect more than one angle?

Yes, a vector c can bisect multiple angles if it is placed at the vertex of those angles and divides them equally.

## 4. Is vector c always perpendicular to the angle it bisects?

No, vector c is not always perpendicular to the angle it bisects. It can be parallel to one of the angle's sides, depending on the angle's measure and the vectors a and b.

## 5. What are some real-world applications of finding a vector c that bisects an angle?

One example is calculating the velocity of an object as it changes direction in motion. Another is determining the direction of an incoming force or impact on a structure. It can also be used in navigation and surveying to find the direction of a point or object in relation to other points.

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