The vector `veca+vecb` bisects the angle between the non-collinear vectors `vecaandvecb`, if……..

Explanation

If vector `veca+vecb` bisects the angle between the non-collinear vectors, then
`veca.(veca+vecb)=|veca|.|veca+vecb|costheta`
`veca.(veca+vecb)=asqrt(a^(2)+b^(2))costheta`
`impliescostheta=(veca.(veca+vecb))/(asqrt(a^(2)+b^(2)))......(i)`
`vecb.(veca+vecb)=|vecb|.|veca+vecb|costheta`
and `vecb.(veca+vecb)=bsqrt(a^(2)+b^(2))costheta` [since, `theta` should be same]
`impliescostheta=(vecb.(veca+vecb))/(bsqrt(a^(2)+b^(2)))........(ii)`
From Eqs. (i) and (ii),
`(veca.(veca+vecb))/(asqrt(a^(2)+b^(2)))=(vecb.(veca+vecb))/(bsqrt(a^(2)+b^(2)))implies(veca)/(|veca|)=(vecb)/(|vecb|)`
`:.hata=hatbimplieshataandhatb` are equal vectors.