Calculate F. dS where F = (4r*z, 4y°z, 324) and S is the surface of the solid bounded by the hemispheres z = 16 – a² – y², z 4 – a? – y? - and the plane z = 0.

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.)

Determine the intersection point of the line​x=7−ty=2+tz=4−3t​ and the plane π:x+2y+3z−15=0

A surface is defined by the following equation: 9x2 + 16y2 + 9z2 = 25. Sketch the intersection between this surface and the xy, xz, and yz planes.