Given that tissue homogenization with an OMNI TH metal-bladed probe is a very violent disruption of tissue in Trizol (with apparently no effect on RNA integrity - as I have found by Bioanalyzer analysis of RNA afterwards), vortexing would be considered a very mild/minimal disturbance to extracted RNA. So I would not worry at all that your RNA has been fragmented by mechanical disruption by mere vortexing. The bigger thing to worry about would be contaminating tissue RNAses during inappropriate storage time-periods - degrading your RNA.
I don't think shearing via vortexing is a legitimate concern. Maybe it would be more of a problem if you were using oligo dt. But I've never vortexed samples for greater than 1min and have no data to back up my claim. If you're doing RT-qPCR avg recommended fragment size is 100bp so as you can imagine, sheared RNA isn't a problem for such an application.
Thanks for your answers discussion with technical senior scientist at invitrogene technical support say to me that the problem of vortex is that we dont mix enough our trizol chlorophorm and he recommended to me manual agitation. I am surprised by this answer.
Everyone is correct. Vortexing will not shear your RNA to make it unusable if you are doing random priming RT - only if you want to clone long mRNA. The Invitrogen tech support is correct as well. Chloroform is heavier than Trizol and will sink to the bottom of the tube. If you do not mix well before vortexing (by rapid inversion with shaking) then you can sometimes find that you can get the two phases being vortexed but not mixing, except at the interface (I have noticed this - the phases separate out very quickly and are not so "milky"). Good removal of protein and DNA relies up good mixing Shake before you vortex - the same applies when you are doing ethanol / IPOH precipitations.