If ` vec r=( hat i+2 hat j+3 hat k)+lambda( hat i- hat j+ hat k)a n d vec r=( hat i+2 hat j+3 hat k)+mu( hat i+ hat j+ hat k)` are two lines, then find the equation of acute angle bisector of two lines.

Explanation

Lines are `vecr=(hati+2hatj+3hatk)+lamda(hati-hatj+hatk) and vecr=(hati+2hatj+3hatk)+mu(hati+hatj-hatk)`
along vectors `(hati-hatj+hatk) and (hati+hatj-hatk)`, respectively.
`" "` Angle between two lines = `cos^(-1)""(((1)xx(1)+(-1)(1)+(1)(-1))/(sqrt(3)sqrt(3)))=cos^(-1)(-(1)/(3))`
which is an obtuse angle.
`therefore" "` Vector along acute angle bisector = `lamda[(hati-hatj+hatk)/(sqrt(3))-(hati+hatj-hatk)/(sqrt(3))]=(2lamda)/(sqrt(3))(-hatj+hatk)`
`therefore" "` Equation of acute angle bisector = `(hati+2hatj+3hatk)+t(hatj-hatk)`