Question

If `A= <3, -1 >` and `B= <9, 4 >`, what is `||A+B|| -||A|| -||B||`?

Answer 1

The answer is `=-0.64`

Explanation:

The vectors are

`vecA= <3,-1>`

`vecB = <9,4>`

The modulus of `vecA` is `=||vecA||=||<3,-1>||=sqrt(3^2+(-1)^2)=sqrt(9+1)=sqrt10`

The modulus of `vecB` is `=||vecB||=||<9,4>||=sqrt(9^2+(4)^2)=sqrt(81+16)=sqrt97`

`vecA+vecB= <3,-1> + <9,4> = <12,3>`

The modulus of `vecA+ vecB` is `=||vecA+ vecB||=||<12,3>||=sqrt(12^2+(3)^2)=sqrt(144+9)=sqrt153`

Therefore,

`||vecA + vecB||-||vecA|| -||vecB||=sqrt153-sqrt10-sqrt97= -0.64`