MATH 102 Final, Fall 2002

LEBK a i or suRoT American University of Beirut Math 102 Dr. H. Yamani Final Exam Name: Fall 2003 ****GOOD LUCK**** 1 Determine each of the following. (= —x? +2x dx x42 AD ft. : * LIbR OG. OF BEKOT 3 2 What curve is given by the following parametric representations x=3 +2 Cos2t y=5+3 Sin 2t 3 Find the equation of the plane through the point (2,4,5) perpendicular to the line x=54t, y= 1+ 3t, z=4t + Find the area of a triangle with vertices P(1, 3, 2) , Q( 2,1,-1) , R(-3,1,5) 5 Find the angle between the planes 2x +2y — z= 3, x +2yt+z=2 eke 1” aa LEE? : oF BEAT 6 Find the length of the curve r = cos*( 6/3), O<sO<2/4 7, Find the area of the region shared by the circles r= 4 cos@ andr =4 sin6 8. A force F = 2i +j -3k Newtons is applied to a spacecraft with velocity vector v = 3i—j. Express F as a sum of a vector parallel to v and a vector orthogonal to v.