We propose to study the a_0(980) and the Λ(1670) resonances in the Λ^+_c →π^+ ηΛ decay via the final state interactions of the π^+ η and ηΛ pairs. The weak interaction part proceeds through the c quark decay process: c(ud) → (s + u + d̅)(ud), while the hadronization part takes place in two different mechanisms. In the first mechanism, the sud cluster picks up a qq̅ pair from the vacuum to form the ηΛ meson-baryon pair while the ud̅ pair from the weak decay hadronizes into a π^+. In the second,

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... he sud cluster turns into a Λ, while the ud̅ pair from the c decay picks up a qq̅ pair and hadronizes into a meson-meson pair (πη or KK̅). Because the final π^+ η and ηΛ states are in pure isospin I = 1 and I=0 combinations, the Λ^+_c →π^+ ηΛ decay can be an ideal process to study the a_0(980) and Λ(1670) resonances. Describing the final state interaction in the chiral unitary approach, we find that the π^+ η and ηΛ invariant mass distributions, up to an arbitrary normalization, show clear cusp and peak structures, which can be associated with the a_0(980) and Λ(1670) resonances, respectively. The proposed mechanism can provide valuable information on the nature of these resonances and can in principle be test by facilities such as BEPCII.