Hi everyone, I got a question here and I think I have solved it, but I just feel the my answer is so messy, can anyone tell me if my answer is right please?
Find the tangent plane to the torus
where at the point
My answer is
Am I right? It looks so weird.
I just wonder how did you check the answer? Because I was thinking maybe I can subsititute the points (I mean my answer) back to the question and see if it fits the original question, but I didn't know how to do it.
So how did you check it? Where can you subsititute back and you found it should be -32 instead of 32? Thanks a lot.
However,after I change it become negative 32,the first two terms in left side is multiple of instead of ,so I still cannot simplyfy.Could you please help me?Thanks a lot.
I used exactly same methods as you.I calculated two tangent vectors with respect to , and , and I also got exactly same answer when I subsititute to find they are ,and
Except when I calculated normal vector,you end up with something quite simple and nice,but I still had three nasty and complicated numbers, than I used the formula , but did not end up same thing as you.
I will double check my work and calculation,I may made mistakes since the numbers are weird. Thanks again for your time.