What is Permethrin kill spider too?

Yes, it will kill spiders too. I am not a big fan of killing spiders unless they are a nuisance. It's kind of like bees. Spiders are very beneficial in their own way, nature's bug killing machines. I shoo them outside, when I can, if they are outside, I leave them alone. Sometimes you just have to, I understand, but please think first. Don't kill spiders or bees unless you really have to, and if you do, it's not hard, any insect killer, or even a good shot of WD 40 will do it.

Permethrin is an insecticide. Yes, it will kill spiders. Some of it is labeled for use on dogs. I heard on a gardening show that if you spend a lot of time in mosquito infested areas, you could buy a spare washing machine and use permethrine in it and your clothes will kill mosquitos that land on them. But you don't want permethrine on everything you own so that's why you should only do it if you have a second washing machine.

It will, but why, spiders are a great natural exterminator themselves.
Don't care what labels say about safe, if it can kill bugs, it is not safe for humans and pets. I know this watching my mother suffer emphysema from pesticide exposure.
Trust me, spiders are more your friend than your enemy, they are not the bad guys.
I keep bees so pesticides are banned from my property, and my spiders do a great job of getting rid of pest bugs.
If you feel you just must kill spiders, even a mix of water and liquid dish soap will kill them if you spray them directly.
Non toxic, safe for the environment, and doesn't kill everything good or bad.
55 years, and never once ever 'HAD' to kill a spider.