Consider the inner product defined by polarizing the quadratic form $$q(x,y,z)=x^2-z^2+4xy-2yz$$ on $\mathbb{R}^3$.

Let $V=\langle(1,0,2),(3,-1,0)\rangle$. Could you show me how to find $V^\bot$ and $V\cap V^\bot$? I get $V^\bot=\langle(2,6,1)\rangle$, which doesn't feel right, and don't know how to calculate the intersection. Also, in general, what can we say about the dimension of $W^\bot$ if we know the dimension of $W$?


Question: What are the pitfalls of buying a used car after an accident?
Answer: One indicator in this case could be the airbags. In a frontal accident they deploy if the impact was strong enough. So I'd consider the car if the airbags are still the originals. Too big of a chance of structural damage if the airbags deployed and were replaced. Better to steer clear…