In a given vector space with 2 differently defined inner products, will an orthogonal vector by 1 necessarily by orthogonal by the other, I'm thinking yes.
@MathTheBeautiful : You need to banish the phrase "If you really think about it" from your teaching vocabulary. Why? Well, you need to really think about it.
See? I can't watch your video... Let this comment be a timestamp, I will revisit this video until I can see it properly, replying to this comment as a second timestamp. Note: an ad played smoothly before the video started.