If A= <-3, -1 > and B= <4, 5 >, what is ||A+B|| -||A|| -||B||?

1 Answer
Jul 1, 2018

||A+B|| - ||A|| - ||B|| = color(crimson)(sqrt(17)-sqrt(10)- sqrt(41) ~~ - 5.4423

Explanation:

A=((-3),(-1))

B=((4),(5))

A+B=((-3),(-1)) +((4),(5))=((1),(4))

||A+B||=sqrt((1)^2+(4)^2)=sqrt(17)

||A||=sqrt((-3)^2+(-1)^2)=sqrt(10)

||B||=sqrt((4)^2+(5)^2)=sqrt(41)

:.||A+B|| - ||A|| - ||B|| = color(crimson)(sqrt(17)-sqrt(10)- sqrt(41) ~~ - 5.4423