If $A= <-3, 6 >$ and $B= <-2, 5 >$ , what is $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2017-12-16T09:30:04

The answer is $=-0.01$

The vectors are

$vecA= <-3,6>$

$vecB = <-2,5>$

The modulus of $vecA$ is $=||vecA||=||<-3,6>||=sqrt((-3)^2+(6)^2)=sqrt(9+36)=sqrt45$

The modulus of $vecB$ is $=||vecB||=||<-2,5>||=sqrt((-2)^2+(5)^2)=sqrt(4+25)=sqrt29$

The modulus of $(vecA+vecB)$ is

$||vecA+vecB||= ||<-3,6,> +<-2,5>|| =||< -5,11>||$

$=sqrt((-5)^2+11^2)$

$=sqrt(25+121)$

$=sqrt146$

Therefore,

$||vecA+vecB||-||vecA|| -||vecB||=sqrt(146)-sqrt(45)-sqrt(29)= -0.01$

If A= <-3, 6 >A= <-3, 6 > and B= <-2, 5 >B= <-2, 5 >, what is ||A+B|| -||A|| -||B||||A+B|| -||A|| -||B||?