If $A= <6, -1 >$ and $B= <-7, 5 >$ , what is $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2016-12-02T15:31:00

The answer is $=sqrt17-sqrt37-sqrt74$

It is just calculating the sum and modulus of vectors.

$vecA+vecB=〈6,-1〉+〈-7,5〉=〈-1,4〉$

The modulus of

$vecA+vecB=∥〈-1,4〉∥=sqrt(1+16)=sqrt17$

The modulus of

$vecA=∥〈6,-1〉∥=sqrt(36+1)=sqrt37$

The modulus of

$vecB=∥〈-7,5〉∥=sqrt(49+25)=sqrt74$

So,

$∥vecA+vecB∥-∥vecA∥-∥vecB∥$

$=sqrt17-sqrt37-sqrt74$

If A= <6, -1 >A= <6, -1 > and B= <-7, 5 >B= <-7, 5 >, what is ||A+B|| -||A|| -||B||||A+B|| -||A|| -||B||?