Question

Find the vector of magnitude 3, bisecting the angle between the vectors `veca=2hati+hatj-hatk and vecb=hati-2hatj+hatk`.

Answer 1

A vector bisecting the angle between `veca and vecb` is `(veca)/(|veca|)pm (vecb)/(|vecb|)`.
Here `" "(2hati+hatj-hatk)/(sqrt6)pm (hati-2hatj+hatk)/(sqrt6)`
i.e., `" "(3hati-hatj)/(sqrt6) or (hati+3hatj-2hatk)/(sqrt6)`
A vector of magnitude 3 along these vectors is
`" "(3(3hati-hatj))/(sqrt(10)) or (3(hati+3hatj-2hatk))/(sqrt(14))`