Find a vector parametric equation r(t) for the line through the points P = (4, -3, 4) and Q = (3, −6, 2) for each of the given conditions on the parameter t. (a) If 7 (0) (4, −3, 4) and 7(2) = (3,−6, 2), then r(t) = <4- -3 t 2 9 = (b) If 7(6) r(t) = <7 = P and 7(8) = Q, then 2,6-3,10-t> (c) If the points P and Q correspond to the parameter values t = 0 and t = -4, respectively, then = r(t) = <4 t 9 31,4-t> 2 -3 - 3t ‚,4 -> 4'

16. Find both the vector equation and the parametric equations of the line through (-2,2,8) and (1, - 4,0), where t =0 corresponds to the first given point. The vector equation is (x,y,z) = + (1). Find the parametric equations of the line through (-2,2,8) in the direction from (-2,2,8) toward (1,-4,0). The parametric equations are x = (Use the answer from the previous step to find this answer.) y%3D (1) O t(3,-6,-8). O t(-6,3,-8). O t(-8,-6,3). O t(-8,3,-6). 17. If possible, find the absolute maximum and minimum values of the following function on the region R. f(x,y) = 5 e-X-Y; R={(x,y): x20, y2 0} Determine the absolute maximum value of f(x,y) on R. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The absolute maximum value of f on R is O B. The function f(x,y) has no absolute maximum value on R. Determine the absolute minimum value of f(x,y) on R. Select the correct choice below and, if necessary, fill in the answer box to…

Take the parametric equations of the lines [x/13 = y/3 = z/8] and [x-11/-10 = y-3/-4 = z-8/-7]; Find the scalar equation of the lines in the form of ax+by+cz+d=0  Show how to check that (13,3,8) fits the equation of the plane. Show how to check how (0,0,0) fits the equation of the plane. Show to to check that (1,-1,1) fits the equation of the plane.