Solve the problem if u and v and w evaluate uwvw show all

Solve the problem

if u = <-5,3> and v=<-4,-6> and w=<-3,12> ; evaluate u*w+v*w

show all steps and work clearly please

answer:-9

given

u = <-5,3> and v=<-4,-6> and w=<-3,12>

to find u*w+v*w

we can write u = -5i +3j and v = -4i -6j and w =-3i +12j

in the dot proudct i.i =1 and j.j =1 and for remaining i.j =j.i =0

so u*w = (-5i +3j) . (-3i +12j)

= (-5).(-3) + 3.12

=15 +36

=51

now we find v*w = (-4i -6j). (-3i +12j)

= (-4).(-3) + (-6).(12)

=12 -72

=-60

now add u*w+v*w = 51 -60

u*w+v*w = -9