Page%1%of%3%MAT10720 Linear Algebra Assignment 3 Session 2 in 2017 Assessing content from topics 5-9 Due

Page%1%of%3%MAT10720 Linear Algebra Assignment 3 Session 2 in 2017 Assessing content from topics 5-9 Due:17th September 2017 Total marks: 66 QUESTION 1 Vector Basics a.%Determine whether the vectors !”=1,2,3,!(=?1,2,?1and–!.=(?1,1,3) form an orthogonal set.%3 marks%b.%Calculate the norm of !=(8,?6) and find the unit vector in the same direction as !.%2 marks%c.%Determine whether the points 3″=(?1,2,2),3(=(3,3,4),3.=(2,?2,10) and 36=(0,2,2) lie on the same plane using the scalar triple product.%4 marks%d.%Determine the angle in radians between 7″=2,4,?5and–7(=(?1,3,?2).%3 marks%e.%Find a vector parallel to 7=(4,?9,3,0,8) in ?;. 1 mark%f.%Calculate the cross product of !”=(2,1,?3),!(=(0,4,5). What is the angle between the resulting vector and !”, and the resulting vector and !(? 3 marks%g.%Find the vector component of 7 along < and the vector component of 7 orthogonal to < for 7=(7,?2,3)-and-