If `vec(a)=7hat(i)-4hat(j)-4hat(k)` and `vec(b)=-2hat(i)-hat(j)+2hat(k)`, determine vector `vec(c)` along the internal bisector of the angle between vectors `vec(a)` and `vec(b)` such that `|vec(c)|=5sqrt(6)` .

Answer

`vec(c)=+-(5)/(3)(hat(i)-7hat(j)+2hat(k))`