MATH 599 Final: MATH 5B UCSB 5B Fall 06 5bFinalSolutions
Document Summary
1. (a) find parametric equations for the line that passes through the point (2, 0, 1) and is perpendicular to the plane with equation 4x y 2z = 1. The direction vector for this line is v = (4, 1, 2) and it must pass through the point (2, 0, 1). L1 : x = 1 + 2t y = 3 2t z = 3t. Since the plane contains the two lines, their direction vectors (1, 1, 0) and (2, 2, 3) are parallel to the plane. Hence their cross product will be a normal vector. = 3i 3j + 0k = ( 3, 3, 0). n = (1, 1, 0) (2, 2, 3) =(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) j k i. To get a point in the plane, we can take any point in either line, so just set t = 0 in the equations for l1 to get the point (0, 2, 3).
