If $A= <-1, 2 >$ and $B= <-3, 4>$ , what is $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2017-01-04T11:04:33

The answer is $=-0.025$

$vecA+vecB=〈-1,2〉+〈-3,4〉=〈-4,6〉$

The modulus of $vecA$ is $=∥vecA∥=∥〈-1,2〉∥=sqrt(1+4)=sqrt5$

The modulus of $vecB$ is $=∥vecB∥=∥〈-3,4〉∥=sqrt(9+16)=sqrt25=5$

The modulus of $vecA+vecB$ is $=∥vecA+vecB∥=∥〈-4,6〉∥=sqrt(16+36)=sqrt52$

Therefore,

$∥vecA+vecB∥-∥vecA∥-∥vecB∥=sqrt52-sqrt5-5=-0.025$

If A= <-1, 2 >A= <-1, 2 > and B= <-3, 4>B= <-3, 4>, what is ||A+B|| -||A|| -||B||||A+B|| -||A|| -||B||?