The correct option is A d→Ldt is perpendicular to →L at all times.
Due to law of conservation of angular momentum, →L= constant
i.e. →L.→L = constant
or, ddt(→L.→L)=0
or, 2→L.d→Ldt=0
or, →L⊥d→Ldt
Since τ=→A×→L
d→Ldt=→A×→L
i.e., d→Ldt must be perpendicular to →A as well as →L.
Further the component of →L along →A is →A.→LA. Also
ddt(→A.→L)=→A.d→Ldt+→L.d→Adt=0 {∵→A⊥d→Ldtandd→Adt=→0}
or, →A.→L = constant
i.e., →A.→LA = x = constant
Since d→Ldt (or τ) is perpendicular to →L, hence it cannot change magnitude of →L but can surely change direction of →L.