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DATE: Dec 14th, 2017DEPARTMENT & COURSE NO: MATH1300EXAMINATION: Vector Geometry and Linear AlgebraINTERNATIONAL COLLEGE OF MANITOBAFINAL EXAMINATIONTITLE PAGETIME: 2 hoursEXAMINER: I. SolimanFamily 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 workand justify your answers. Unjustifiedanswers will receive LITTLE or NOCREDIT.No texts, notes, or other aids arepermitted.Calculators, cell phones,electronic translators, and other electronicdevices arenotpermitted.This exam has a title page, 9 pages ofquestions, and 1 blank pages for rough work(a total of 11 pages). Please check that youhave all the pages. You may remove theblank pages if you want, but be careful not toloosen the staples.The value of each question is indicated besidethe statement of the question. The totalvalue of all questions is 87 marks.If you need more scrap paper, use the back ofthe pages.QuestionMarksScore11221031541651569710Total:87
DATE: Dec 14th, 2017DEPARTMENT & COURSE NO: MATH1300EXAMINATION: Vector Geometry and Linear AlgebraINTERNATIONAL COLLEGE OF MANITOBAFINAL EXAMINATIONPAGE: 1 of 11TIME: 2 hoursEXAMINER: I. Soliman1. Let-→v= [3,1,-1],-→u= [2,0,1] and-→w= [k,2-k,1 +k]. Find all the value(s) ofksuchthat(a)-→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)-→wis perpendicular to the vector components of-→vorthogonal to-→u.