Question

If `A= <-3, -1 >` and `B= <-2, 5 >`, what is `||A+B|| -||A|| -||B||`?

Answer 1

`||A+B||-||A-B||=sqrt41-sqrt37`

Explanation:

`A=(A_x,A_y,A_z)" "B=(B_x,B_y,B_z)`
`A+B=(A_x+B_x,A_y+B_y,A_z+B_z)`
`A-B=(A_x-B_x,A_y-B_y,A_z-B_z)`
`A+B=(-5,4)`
`A-B=(-1,-6)`
`||A+B||=sqrt((-5)^2+4^2)=sqrt(25+16)=sqrt41`
`||A-B||=sqrt((-1)^2+(-6^2)=sqrt(1+36)=sqrt(37)`
`||A+B||-||A-B||=sqrt41-sqrt37`