Math 1540 Trigonometry Solution To Midterm Exam Pp

This study source was downloaded by 100000857300661 from CourseHero.com on 11-17-2022 01:09:14 GMT -06:00https://www.coursehero.com/file/122568312/Solution-to-Midterm-Exam-PPpdf/ THE CHINESE UNIVERSITY OF HONG KONGDEPARTMENT OF MATHEMATICSMATH1540 University Mathematics For Financial Studies 2021-2022 Solution to Midterm Examination Time allowed: 90 minutes Total points: 50 points Answer all questions1.Let L:r(t) = ( 1, 4,2) + t(1 ,1 , 2) be a straight line and let : 2 x+ 3 y z= 5 be a plane in R3.(a)Find the intersection point of Land .(b)Find the equation of straight line lying on which passes through the intersection point found in (a), and is also perpendicular to L.(5 points)Ans: (a)Put x= 1 + t, y = 4 + tand z= 2 2t into the equation of , then2( 1 + t) + 3( 4 + t) (2 2t) = 57 t = 21t = 3Therefore, the intersection point of Land is (2 , 1, 4).(b)Note that n= (2 ,3 , 1) gives a normal vector of and a= (1 ,1 , 2) gives a direction vector of L.Therefore, n a= ( 5,3 , 1) gives a direction vector of the required straight line. Then, the requiredstraight line isr(s ) = (2 , 1, 4) + s( 5,3 , 1)