Need understanding of unit vector bisectors

[Nelle91]

Hey, i was wondering if anyone could please help me with the following question

The position vectors of points A and B are a=i - j - k and b=2i - 2j -2k

Find the unit vector which bisects (angle) AOB

It would be much appreciated if it had some instructions on how to get to the solution.
Much appreciated

[Umesh]

arent those vectors on the same line?

[unknown id]

yea, r u sure u copied the question out correctly?

[Nelle91]

yeah sorry guys its meant to be a= i - j + k

[unknown id]

make sure u recognise that adding unit vector OA with unit vector OB gives u the vector that bisects angle AOB. u can then find this unit vector as per usual (by multiplying the vector with the reciprocal of its magnitude). i'd recommend u try drawing it, it will make more sense.

[Nelle91]

How did you work out adding the unit vectors of a and b give the vector that bisects angle AOB, is just something you need to know?

[unknown id]

it makes sense intuitively. for example:

let's take unit vector OA:    ----->

and unit vector OB:    ^
                              |
                              |
                              |
                              |

To find the vector that bisects angle AOB, add these two unit vectors together:

           ^      ^
           |      /
           |    /
           |  /
           |_ _ _ _ >

so that the resultant vector bisects the angle AOB. this also works for any two non-perpendicular vectors, given that u add only their unit vectors together

(ps. sorry for the crap diagrams)

[VCEforthewin]

Oh, thanks alot I think I understand it now, much in your debt

This is the nelle91 btw

[Mao]

wow, thank you unknown id.

i never knew that =D

[Collin Li]

Yep, it's especially important that you add their unit vectors, or vectors of equal magnitude.

If you don't then one vector's direction will weigh more heavily than the other's, and hence you will not get a perfect bisection. You will get some vector in between the two, but not a bisecting vector.

[xox.happy1.xox]

Wow, I actually think this is interesting!