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#