If `veca=7hati-4hatj-4hatk and vecb=-2hati-hatj+2hatk`, determine vector `vecc` along the internal bisector of the angle between vectors `veca and vecb` such that `|vecc|= 5sqrt6`.

Explanation

`hata=(1)/(9)(7hati-4hatj-4hatk)`
`" "hatb=(1)/(3)(-2hati-hatj+2hatk)`
`" "vecc=lamda[hata+hatb]=lamda(1)/(9)(hati-7hatj+2hatk)`
`" "|vecc|=5sqrt(6)`
`rArr" "(lamda^(2))/(81)(1+49+4)=25xx6`
`" "lamda^(2)=(25xx6xx81)/(54)=2225`
`" "lamda=pm15`
Putting the value of `lamda` in (i), we get
`" "vecc=pm(5)/(3) (hati-7hatj+2hatk)`