If A= <-7, 6 > and B= <-3, 8>, what is ||A+B|| -||A|| -||B||?

1 Answer
Aug 1, 2016

||A+B||-||A||-||B||=sqrt296-sqrt85-sqrt73

~=-0.56.

Explanation:

# A=<-7,6>, B=<-3,8>

rArr ||A||=sqrt{(-7)^2+6^2}=sqrt(49+36)=sqrt85, and,

||B||=sqrt(9+64)=sqrt73>.

A+B=<-7-3,6+8>=<-10,14>

:. ||A+B||=sqrt(100+196)=sqrt296.

Hence, ||A+B||-||A||-||B||=sqrt296-sqrt85-sqrt73

~=17.20-9.22-8.54=-0.56.