Question

If `A= <7 , 2>` and `B= <-7, -1 >`, what is `||A+B|| -||A|| -||B||`?

Answer 1

`color(red)||A+B|| - color(blue)(||A|| -||B||) = color(red)1-color(blue).209 ~~ .791`

Explanation:

Given:`A= <7 , 2>` and `B= <-7, -1 >`,
Required: `color(red)||A+B|| - color(blue)(||A|| -||B||)`
The red is the magnitude of the vector addition and the blue is
the sum of the magnitude of vectors.
`color(red)(Red)`
`vec(A)+vec(B) = <0, 1>`
and the magnitude is: `color(red)(||A+B||=1)`

`color(blue)(Blue)`
`||A||= sqrt(7^2+2^2) =sqrt(53)`
`||A||= sqrt(7^2+1^2) =sqrt(50)`
`color(blue)(||A|| -||B||=sqrt(53)-sqrt(50)~~ .209`

`color(red)(Red)-color(blue)(Blue) = color(red)1-color(blue).209 ~~ .791`

Answer 2

`||A+B|| - ||A|| - ||B|| = color(orange)(13.3512`

Explanation:

`A=((7),(2))`

`B=((-7),(-1))`

`A+B=((7),(2)) +((-7),(-1))=((0),(1))`

`||A+B||=sqrt((0)^2+(1)^2)= 1`

`||A||=sqrt((7)^2+(2)^2)=sqrt(53)`

`||B||=sqrt((-7)^2+(-1)^2)=sqrt(50)`

`:.||A+B|| - ||A|| - ||B|| = color(orange)(1-sqrt(53)- sqrt(50) ~~ - 13.3512`