- #1

Andy13

- 16

- 0

## Homework Statement

Find a vector v that bisects the smaller of the two angles formed by 3i+4j and 8i-15j.

## Homework Equations

dot product: cos(theta)= u*v/(||u|| ||v||)

## The Attempt at a Solution

I first found the angle in question by putting the two given vectors into the dot product cosine formula. This was the smallest angle.

My next step was to try to do the same thing with some unknown vector, one of the knowns, and the angle I just found, but it turned into an algebraic nightmare. Thoughts? Method is below, except without a true value for theta or cos theta because I forgot what it was off the top of my head-- I've been trying to think about how it would work without numbers first.

Known: angle theta, vector <3,4>

Assume unknown vector (ai+bj)

cos(theta)=((3a+4b)/(5*sqrt(a^2+b^2))

Thanks.