Find equations for (a) the tangent plane and (b) the normal line at point Po (0,3,4) on the surface 7 cos (RX) - 4x y + 4exZ + 3yz = 47. . . . (a) Using a coefficient of 16 for x, the equation for the tangent plane is (b) Select the equations for the normal line. O A. X= - 16t y =3- 12t O B. x = 16t Z =4 - 9t y =3-12t Z =4 - 9t O C. x = 16t y =3+12t OD. X= - 16t Z =4+9t y =3+12t Z =4+ 9tFind the directions in which the function increases and decreases most rapidly at P . Then find the derivatives of the function in these directions. f(x,y,z) = (x/y)- yz, Po( - 4, - 1, -4) . . . The direction in which the given function f(x,y,z) = (x/y) - yz increases most rapidly at Po( - 4, - 1, - 4) is u = i+ ( Dj + ( )k. (Type exact answers, using radicals as needed.) The direction in which the given function f(x,y,z) = (x/y) - yz decreases most rapidly at Po ( - 4, - 1, - 4) is v = |ji+ (j +( )k. (Type exact answers, using radicals as needed.) The derivative of the given function f(x,y,z) = (x/y) - yz in the direction in which the function increases most rapidly at Po ( - 4, - 1, - 4) is Duf =]. (Type an exact answer, using radicals as needed.) The derivative of the given function f(x,y,z) = (x/y) - yz in the direction in which the function decreases most rapidly at Po( - 4, - 1, -4) is Dyf =. (Type an exact answer, using radicals as needed.)K Find parametric equations for the line tangent to the curve of the intersection of the surfaces x+ 2x y+ y+ 12xy -z = 0 and x + y + z = 18 at the point P(1, 1, 4). Select the parametric equations for the tangent line. O A. X =1 + 168t y = 1 - 168t O B. X= 1 - 168t Z = 4 y = 1 + 168t Z =4 O C. x= 19t y = 1 - 19t O D. X = 1+ 19t z=4 y=1- 19t Z = 4 + 19t