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

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Answer 1 · 2017-11-21T09:32:15

The answer is $=-0.64$

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,

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

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