Let F(x, y, z)=-y²i+xj+2²k, and let the curve C' be the intersection of the paraboloid z = ² + y² with the plane z = 20 - 2x - 4y, oriented counter-clockwise when viewed from above. Evaluate F. dr by

Find the coordinates of the point (x, y, z) on the plane z = 4 x + 1 y + 2 which is closest to the origin. X = y = Z =

1) Find the distance from the point (1, 2, 3) to the (a) XZ plane (b) Z axis

The paraboloid z = 6 - x - x² – 2y² intersects the plane x = 3 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (3, 3, -24). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)