Let wr₁ (t) =< t, t² > and r₂(t) =. Find (r₁(t)- r₂(t)). O<3t²,8t²> 04t² +6t³ 0312 +8+4 0<4²,64³ >

x = (a) Find the distance from the point A(-2, -4, 2) to the line L −3+ 5t, y = −2 − 1t, z = −2 - 3t. 4.503 (b) The closest point to A on L is

Find the mass M of a fluid with a constant mass density flowing across the paraboloid z = 36 - x² - y², z ≥ 0, in a unit of time in the direction of the outer unit normal if the velocity of the fluid at any point on the paraboloid is F = F(x, y, z) = xi + yj + 13k. (Express numbers in exact form. Use symbolic notation and fractions where needed.) M = Incorrect 31740πσ > Feedback Use A Surface Integral Expressed as a Double Integral Theorem. Let S be a surface defined on a closed bounded region R with a smooth parametrization r(r, 0) = x(r, 0) i + y(r, 0) j + z(r, 0) k. Also, suppose that F is continuous on a solid containing the surface S. Then, the surface integral of F over S is given by [[F(x, y, z) ds = = D₁² Recall that the mass of fluid flowing across the surface S in a unit of time in the direction of the unit normal n is the flux of the velocity of the fluid F across S. M = F(x(r, 0), y(r, 0), z(r, 0))||1r × 1e|| dr de F.ndS X

1 dt 3/2 t² +9 2.