20. [-/5 Points] DETAILS LARCALC11 11.7.029. Find an equation in rectangular coordinates for the surface represented by the cylindrical equation. r = 14 sin(0) Sketch its graph. Z 10 z 1 10 10 -10 - 10 - 10 10 10 10 10 10 -10_ 10 O O 10 -10 -10 10 10 -10 -10 10 -10) 1018. [-/5 Points] DETAILS LARCALC11 11.7.006. Convert the point from cylindrical coordinates to rectangular coordinates. 6 , 5 2 ( x , y, z) = 19. [-/5 Points] DETAILS LARCALC11 11.7.010. Convert the point from rectangular coordinates to cylindrical coordinates. (9, 3V3, -6) (r, 0, z) =LARCALC11 11.6.012. DETAILS 17. [-/5 Points] Describe the surface. yz + z = 5 The ? v -coordinate is missing so it is a -Select- v cylinder with the rulings parallel to the ? ~ | -axis. The generating curve is a [-Select-~] Sketch the surface. 10 -2 10 -10 10 -5 O 10 -5 70 5 - 10 10 1016. [-/5 Points] DETAILS LARCALC11 11.6.005. Match the equation with its graph. x 2 + + 22 = 1 9 16 9 6 - 3 O O N O O 32 O14. [-/5 Points] DETAILS LARCALC11 11.5.009. MY NOTES AS Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.) Point Parallel to (-1, 0, 4) v = 7i + 3j - 9k (a) parametric equations (Enter your answers as a comma-separated list.) (b) symmetric equations oxti y_ 4-z 3 9 0 7x = y = 92 37 O X- 1=y= OX= Y = 15. [-/5 Points] DETAILS LARCALC11 11.5.042. MY NOTES AS Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line. Point Perpendicular to (0, 4, 0) n = -3i + 9k ESC X F9 F1 F2 F3 F4 F5 F6 F7 F8 S % & 3 512. [-/5 Points] DETAILS LARCALC11 11.4.016. Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (10, -18, -2) 13. [-/5 Points] DETAILS LARCALC11 11.5.005. Determine whether each point lies on the line. x = -2 + t, y = 3t, z = 4+t (a) (0, 6, 6) Yes O No ( b ) ( 2 , 3 , 5 ) Yes O No ( C) ( - 4, - 6, 2) O Yes O No(e) u. (3v) 10. [-/5 Points] DETAILS LARCALC11 11.3.018. Find the angle 0 between the vectors in radians and in degrees. (Round your answer for part (a) to three decimal places and part (b) to one decimal place.) u = 2i - 5j + k v = i - 2j + k (a) radians e : (b) degrees 0 = 11. [-/5 Points] DETAILS LARCALC11 11.4.008. Find u x v, v x u, and v x v. U = 41 + 8k v = 3i + 9j - 6k. (a ) uxv ( b vxu (C V X V ESC X Flock F1 F2 F3 F4 F5 FO S