Question

What's the normal to the plane: {x=1+s-t;y=2s-t;-1+s+2t}?

Answer 1

So that is parametrized surface and you want the normal plane at any particular point?

Answer 2

My initial thoughts are just simply denoting two vectors for t and s respectively; and then calculating the cross product from this.

Answer 3

That technically would work, since it is linear.

Answer 4

Yes, I'm not sure if I got the right answer though; as there is no way of checking it in the book.

Answer 5

http://www.wolframalpha.com/input/?i=%5B1%2C2%2C1%5D+cross+product+%5B-1%2C-1%2C2%5D
This is what I get.

Answer 6

Was just about to rewrite my solution; thanks! Was not sure on the syntax of cross products in wolfram! :)

Answer 7

Had an error in the punctuation when calculating the first determinant. :D