Welcome to Gaia! ::

It's true vectors cannot be seen by the human eye, but humans can sense them if they come close enough, you can see them around Mariko's cage, because of the material it's made of. Other diclonii and silpelits can sense them a lot better then humans, their horns also probably help in that case. In the first episode where Lucy beheads that secretary of Kurama, Lucy's vector touched her shoulder and it had blood on it, so you could see the form of the vector's hand.

they cant be seen, they only show them on the show sometimes, just so you understand whats going on

I think it is possible for humans to recognize that the vectors are there in certain condition. But in the anime they said "Yes you can actually see them" about Mariko's vectors and nothing about them having to be in special conditions but then the rest of the time you only see them like the other diclonius' vectors just so you know what is going on. So I don't know what is going on there. If the vectors were covered in something I don't think you can see them because Lucy's vectors are covered in blood but you only see it when it is put on something else. But in conditions such as rain I think perhaps vectors would leave voids where there wouldn't be rain visible and that is possibly how Bondo knew the vectors were coming towards him. I think perhaps vectors being invisible has to do with how fast they vibrate, like a guitar string when it is vibrating you can still see it but it seems to turn almost transparent. Well vectors vibrate so fast that the refresh rate of human eyes can't keep up with it at all so they only see what is behind it. Just a thought anyways no real evidence.

Mariko's vectors were visible because they vibrated so fact that they appeared solid. However, the other diclonius' vectors were of lower energy, and were not visible.

I don't think they can be seen. The doctor, when he brought shirakawa infront of Mariko's tank, said hers could be seen because her wave motions were stronger then the others, (At least I think that's what he said, I dont quite remember. Which explains why Lucy was able to see them, and in return entangle her vectors with Mariko's, allowing Lucy to escape at that point.

Lucy could not see the other vectors. If she could she would have been able to clearly avoid Nana's throw early in the episode where Nana throws Lucy into the shrine. Then again when lucy was sitting on the ground after being thrown, she didn't protect herself when Nana wrapped her vector around her neck. When Nana said she was going to make it so Lucy can't walk, and Lucy looked down, It was probably because she felt the vector enter her leg, like Nana felt Lucy's enter her forhead when they first meet.

and how do you know Kanae saw them? According to her, all she saw was the girl with the horns, and everywhere she went people got hurt really bad.

I think that vectors can't be seen by humans. Because the vectors vibrate they can be sensed by people and animals from certain distances. I think animals can sense them from farther away then people.

Also if they can pick up blood and place hand prints on things they are obviously solid, then since two different things of matter can not occupy the same space, fog or a dust storm or steam, rain, etc... will accumulate around the vectors and instead of actual being able to see the vectors, like a mold you can see the impression they make into other substances.

But I'm pretty sure that humans can't actually see them, not even kanae. See saw people dying around the girl with horns and assumed she was doing something to kill people (She never specified how), Also when she pushed Lucy back she did it because she thought "the girl with horns" was going to kill kohta,the timing of the vecotrs was just a coincidence with her actions.

Diclonius can't see them either, but they can sense them a lot better then any other living beings. of course these are all just my own assumptions based on only the anime.