Question

If `A= <-2, 2 >` and `B= <9, 4>`, what is `||A+B|| -||A|| -||B||`?

Answer 1

`||A+B|| - ||A-B||=sqrt85-sqrt125`

Explanation:

`A+B=C`
`C_x=A_x+B_x=-2+9=7`
`C_y=A_y+B_y=2+4=6`
`||C||=sqrt(C_x^2+C_y^2)" "||C||=sqrt(7^2+6^2)=sqrt(49+36)`
`||C||=sqrt85`

`A-B=D`
`D_x=A-x-B_x=-2-9=-11`
`D_y=A_y-B_y=2-4=-2`
`||D||=sqrt( D x^2+ D y^2)" "||D||=sqrt((-11)^2+(-2)^2)`
`||D||=sqrt(121+4)" "||D||=sqrt125`
`||A+B|| - ||A-B||=||C||-||D||`
`||A+B|| - ||A-B||=sqrt85-sqrt125`