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.
∫cF ⋅ dr = ∫s...
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...
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
I'm really not sure where to start and what process to take to arrive to my answer...