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The decays of χc2→K+K−π0, KSK±π∓ and π+π−π0 are studied with the ψ(3686) data samples collected with the Beijing Spectrometer (BESIII). For the first time, the branching fractions of χc2→K∗K¯¯¯¯¯, χc2→a±2(1320)π∓/a02(1320)π0 and χc2→ρ(770)±π∓ are measured. Here K∗K¯¯¯¯¯ denotes both K∗±K∓ and K∗0K¯¯¯¯¯0+c.c., and K∗ denotes the resonances K∗(892), K∗2(1430) and K∗3(1780). The observations indicate a strong violation of the helicity selection rule in χc2 decays into vector and pseudoscalar meson pairs. The measured branching fractions of χc2→K∗(892)K¯¯¯¯¯ are more than 20 times larger than that of χc2→ρ(770)±π∓, which implies the effects are largely due to U-spin symmetry breaking, rather than just isospin symmetry breaking in charmonium decays.