Let F (x, y, z) z = 3x² + 3y². xyi+xzj+yzk and C be the curve of intersection between the paraboloids with a counterclockwise orientation looking down the positive z-axis. Calculate z = 16x² - y² and F. dr.

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: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: Let C be the positively oriented closed plane curve consisting of the line segment from (-3,0) to…

A:

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Find the coordinates of the point (x, y, z) on the plane z = 4 x + 1 y + 2 which is closest to the…

A:

Q: let C be the curve of intersection of the 3-D graph of x2=2y (a "parobolic cylinder") with the graph…

A:

Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: he paraboloid z = 6 - x - x² - 2y² intersects the plane x = 3 in a parabola. Find parametric…

A:

Q: The paraboloid z = 3 - x - x² - 3y2 intersects the plane x = 4 in a parabola. Find parametric…

A: