How do I find the dot product to show a and b are opposite

Solution

a.b=|a||b|cos

a=<3,4> ==>|a|=[3²+4²]=5

a=<-6,-8> ==>|b|=[(-6)²+(-8)²]=10

<3,4>.<-6,-8>=5*10cos

(3*-6)+(4*-8)=50cos

(-18-32)=50cos

50cos=-50

cos=-1

=180^o

so a=<3,4> and b = <-6,-8> are opposite directions