Assignment Coversheet Student ID number Unit name Engin

Assignment Coversheet Student ID number Unit name Engineering Mathematics 2 Unit number 8225 Assignment name Assignment 2 Due date 5:00 pm Friday November 18 Student declaration I certify that the attached assignment is my own work. I give permission for my assignment to be copied submitted and retained for the electronic checking of plagiarism. Signature of student: ________________________________________ Date: ____________ Assignment feedback Q1 Q2 Q3 TOTAL General comments Date of submission
All working must be shown on you solution sheets. Attach your (hand-written) solutions in natural order to the cover sheet of this assignment. Note: the answers for most problems can be obtained in many ways. Your are welcome to use any method. Some answers can be written in dierent but equivalent forms. Question 1 [5 marks] After a rotation of the primary frame of references the vectors e02 and e03 are proportional to e02 2640 p31 375; e03 264??2p2 ??1 p3 375: (1) Find e01 (2) Find Euler angles of this rotation Question 2 [12 marks] The length of each edge of a pyramid is 1. The square base of the pyramid has the coordinates V1(0; 0; 0); V2(1; 0; 0); V3(0; 1; 0); V4(1; 1; 0) ; see the gure on the next page. (1) Find coordinates of the fth vertex of the pyramid. (2) Find equations for all planes forming the faces of the pyramid. (3) Find all the dihedral angles between these ve planes. (4) Find the distance between the origin V1 and two opposite faces (V3; V4; V5) and (V2; V4; V5). (5) Find the distance from the origin V1 to the edges (V2; V5) (V3; V5) and (V4; V5). (6) For the point X(12; 12; 0) nd its projections to the planes (V1; V2; V5) (V2; V4; V5) (V3; V4; V5) and (V1; V3; V5). Question 2 [8 marks] A quadratic surface is given by equation x2 + y2 + 2xz + 2yz = 1 (1) Find the principal coordinate system for this surface. 1
2 (2) Write the surface equation in principal coordinates. (3) Identify the surface.
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