Dec2016_Math1300_Final-sol.pdf - INTERNATIONAL COLLEGE OF MANITOBA DATE Dec 14th 2017 FINAL EXAMINATION TITLE PAGE DEPARTMENT COURSE NO MATH1300 TIME 2

# Dec2016_Math1300_Final-sol.pdf - INTERNATIONAL COLLEGE OF...

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DATE: Dec 14th, 2017 DEPARTMENT & COURSE NO: MATH1300 EXAMINATION: Vector Geometry and Linear Algebra INTERNATIONAL COLLEGE OF MANITOBA FINAL EXAMINATION TITLE PAGE TIME: 2 hours EXAMINER: I. Soliman Family Name: (Print in ink) Given Name: (Print in ink) STUDENT ID: SIGNATURE: (in ink) (I understand that cheating is a serious offense) INSTRUCTIONS TO STUDENTS: This is 2 hour exam. Show all your work and justify your answers. Unjustified answers will receive LITTLE or NO CREDIT. No texts, notes, or other aids are permitted. Calculators, cell phones, electronic translators, and other electronic devices are not permitted. This exam has a title page, 9 pages of questions, and 1 blank pages for rough work (a total of 11 pages). Please check that you have all the pages. You may remove the blank pages if you want, but be careful not to loosen the staples. The value of each question is indicated beside the statement of the question. The total value of all questions is 87 marks. If you need more scrap paper, use the back of the pages. Question Marks Score 1 12 2 10 3 15 4 16 5 15 6 9 7 10 Total: 87
DATE: Dec 14th, 2017 DEPARTMENT & COURSE NO: MATH1300 EXAMINATION: Vector Geometry and Linear Algebra INTERNATIONAL COLLEGE OF MANITOBA FINAL EXAMINATION PAGE: 1 of 11 TIME: 2 hours EXAMINER: I. Soliman 1. Let-→v= [3,1,-1],-→u= [2,0,1] and-→w= [k,2-k,1 +k]. Find all the value(s) ofksuchthat(a)[4]-→wis parallel to the plane Π : 2x+y-2z=-11. MARKS: 1 mark for the condition of perpendicularity. 1 mark for the normal. 1 mark for the dot product. 1 mark for the final answer. (b)[4]-→wis perpendicular to the vector components of-→vorthogonal to-→u.