Homework Statement
Use Stokes' Theorem to evaluate ∫cF ⋅ dr, where F(x, y, z) = x2zi + xy2j + z2k and C is the curve of the intersection of the plane x + y + z = 1 and the cylinder x2 + y2 = 9 oriented counterclockwise as viewed from above.
Homework Equations
Stoke's Theorem:
∫cF ⋅ dr = ∫s...
Thank you for such a detailed reply! I was also wondering why my teacher calls <0, -1, 3> a directional vector and what significance it holds when using it in problems such as projections or finding lines parallel to planes?
Homework Statement
In most problems involving projections I'm given a vector and the equation of a line either in parametric form or in symmetric form (ie. parametric: <0t+3, -t-4. 3t+2> or symmetric form: x=3, (y+4)/-1, (z-2)/3). However, when asked to use these in a problem I get confused...
So I've thought about this a lot more. This is my thought process. P1: (3,-2,4), P2: (3, -1, 5), P3: t=1: (5, -2, 5). I can then find the vector P1 to P2 and P1 to P3. Use the two vectors I found to do a cross product which will give me the normal vector, which I can then use to come up with the...
Could I possibly set t = 1 and get a point for the line and then use the point and the result I got from t=1 to get a vector? I know I want to get the normal vector from two vectors to get the equation of the plane. Not sure how to get the second vector that's linearly independent. (Just to...
So I know that I need 2 vectors for a plane and currently I'm given a point and a equation of the line. This is the point where I'm unsure of what to do since I don't know how to utilize the tangent vector of the line.
Homework Statement
Problem: Please find an equation for the plane that contains the point <3, -2, 4> and that includes the line given by (x-3)/2 = (y+1)/-1, z=5 (in symmetric form). Simplify
Homework Equations
I'm really not sure where to start and what process to take to arrive to my answer...