6. Let S denote the disc of radius 2 that is centered at the point (0, 0,3) and parallel to the X-Y plane, oriented so that the top of S points in the direction of the negative Z-axis. Compute ff, F. dr where F(x, y, z) = x+sin(y) 2³-xyz z+y-1

Q: Let Z = (1, 1, 2) be a point in R³. Find the closest point to Z tha lies on the plane give by -x+y-z…

A: The normal vector to the plane is <-1, 1, -1>. The point you seek would have to be some…

Q: 8.) Find the planes tangent to the following surfaces indicated points: a:) x² + 2y ²2/3 X ² = 10₁…

A:

Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find an equation of the plane tangent to the…

A: Equation of the plane tangent to the surface  z=f(x, y) at (a, b) is z=fa, b+fxa, b(x-a)+fya, b(y-b)

Q: 10. The point (1, 2, 5) is on the quadric surface z = x² + y². Is this point closer to the line with…

A: Given   1. Point on the quadric surface z=x2+y2 is 1,2,5 2. Parametric equation of the line is…

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

A:

Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

A:

Q: Find the coordinates of L" if ALMN with L(1, 2), M(-2, 6), and N(-1, 5) is rotated 90° about the…

A: Given: L(1,2) , M(-2,6), and N(-1,5)

Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given:

Q: Solve ut + cux=et, u(x,0) = u(x). Draw the characteristics in the x-t plane.

A:

Q: Find the closest point contained in plane 2x + y + 3z = 7 to point S (2, 1, 0). 12) to the plane 2x…

A: