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In the simplest form, in vivo is in a living organism, vs. ex vivo is outside a living organism. Usually in vivo involves an animal model; mouse, rat, gerbil. However, it can also include human testing as well. Ex vivo is less invasive and usually involves testing on living cells or tissue but not the entire animal.
As for vectors. I am familiar with three, but there are multitudes in use. The most commonly used vector is the virus. It is a natural invader of cells and inserts genes into host cells all by itself. Science uses viruses because one only has to add the gene of interest into a virus, then let the virus do all the dirty work of getting that gene into the host cell. There are different forms of virus to use. All are effective but each is used in specific situations. There are also non-viral vector methods. The most common is naked DNA that is injected via a "gene gun". This method is becoming more used as the vector is more stable now than in the past. The third form is oligonucleotides. This is kind of like reversed gene therapy, in that instead of adding a new gene into the mix, oligos are used to block or silence an existing gene. The most common of these is the antisense DNA that blocks the transcription of certain genes. Another method that is very effective is siRNA. This small RNA molecule signals a cell to cleave specific mRNA sequences, disrupting translation of the mRNA and ultimately screws up the expression of a gene.