MATH 252 TEST 1 SPRING, 2004Remember to keep your work neat and orderly. Show all of your work. NO WORK = NO CREDIT! Read each question carefully and be sure to answer the question that was asked. Good luck!Name:____________________________________________________________ ptsvuvu -cosvvvuuwv-21projpoint Q to plane: nnPQD-point Q to line: uuPQDarc length: badtdtdydtdxs221. If  1 2, -1,w and 5- 4, 1,v ,4 3,, 2u, find each of the following:a.uw 23 b. vu -6 5,12,7=-30c. A non-zero vector that is orthogonal to both vu and . 5 11,14,1 d. A unit vector parallel to w, but in the opposite direction. 5 1,2,161 e. The angle between vu and (in radians). 561.2 f. The equation of a line through the point (-6, 8, 7) that is parallel to u. 4473826  zyx (or parametric eqs) g. The equation of a plane normal to v that goes through the point (-3, 5, -8). 40)8(5)5(4)3(  zyx h. The components of uthat are parallel and orthogonal to v. 8par:  7/25,7/20,7/5perp :  7/3,7/1,7/192. Given the parametric equations1 5  txtya. Eliminate the parameter and write y as a function of x. 524 xy b. Give a rough sketch of the graph represented by the parametric equations. Include an arrow to indicate the direction of the curve. Be careful to only include the portion of the graph that is included in the domain of t . 63. Given the parametric equations 293 23522tttyexta. Find dxdy as a function of t. 652224963ttettdxdyb. Find all values of t where the tangent line to the graph is horizontal. 43,1tc. Find all values of t where the tangent line to the graph is vertical. 40t4. Convert the point with rectangular coordinates (-3, 2, 6) to cylindrical coordinates. 6)6,55.2,13(5. Convert the point with polar coordinates (-3, 75) to rectangular coordinates. 6(1.87, -2.35)6. Find the distance between the parallel planes010432  zyx and 0181296  zyx.82947. Find the distance from the point (4, -1, 3) to the line given by .511 ;34 ;27 tztytx 810.83824918. Find the arc length of the portion of the graph of 934 633tytx on the interval .30 t10=