Given vectors u 37 and TeSolutiongiven u w uw 3 42 4

Solution

given u=<-3,7> , w=<1,-6>

u.w = <-3,7>.<1,-6> = - 3 - 42 = - 45

ll u ll = sqrt(9+49)= sqt(58) , ll v ll = sqrt(1+36) = sqt37

angle between vectors cos theta = u.w/llull llwll ]

= -45/[sqt58)sqt37]

=-0.971399

theta = arccos(-0.9714) =166.263

-> 2u = 2<-3,7> =<-6,14>

2u + w = <-6,14> + <1,-6> = <-5,8>

(2u+w).i =  <-5,8>.i = - 5