=== 3. For the vector field = -2zi-2y-2k, find the flux through the ellipsoids: (x²+12+12) (a) (-19)2 + (-18)2 + (8-17)² = 1 15 15 18 (b) (x+1)+(-2)²+(x+3)² = 1

The z-coordinate of the terminal point of the vector v=-5i-19k whose initial point is (-1,-4,-5) is

Find the velocity vector v(t), given the acceleration vector a(t) = (3e¹, 7, 10t +9) and the initial velocity v(0) = (8,-5,3). (Use symbolic notation and fractions where needed. Give your answer in the vector form.) v(t) = 2(e' - 2)i + (3t-2)j + (3r² +9r+2)k Incorrect

Let F = sin(4x +3z) i-6ye*z k. Calculate div (F) and curl (F). (Express numbers in exact form. Use symbolic notation and fractions where needed.) div (F) = (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) curl (F) =

Find the vector equation of the line that contains the points (-5, 17,9) and (-17,10,2). r(t) = ( ) +t ( 9 "

Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

Calculate r' (t) and T(t) and evaluate T(1). r(t) = (6 + 7t,1², 5 – t²) (Give your answers using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) r'(t) = (7,2t,–2t) 7 -2t T(t) = V49 + 8? V49 + 8? Va9 + 8? Incorrect

C only plz

a is 1 and b is 1, you have to use them from the start.

Suppose the straight lines L₁ and L₂ have respective vector equations 5 r1 = -3 + t -0-0--0- and 4 3 where s and t are scalar parameters. 9 = 8 +s -2 -5 -5 2 a) Given that L₁ and L2 intersect at some point P, find its coordinates. P =( )