If A= <2 , 6 > and B= <-1,9 >, what is ||A+B|| -||A|| -||B||?

1 Answer
Narad T.
Nov 8, 2016

The answer is =sqrt226-sqrt82-sqrt40

Explanation:

vecA+vecB=〈2,6〉+〈-1,9〉=〈1,15〉
The modulus of vecA=∥〈2,6〉∥=sqrt(2^2+6^2)=sqrt40
The modulus of vecB=∥〈-1,9〉∥=sqrt(1+81)=sqrt82
Themodulus of vecA+vecB=∥〈1,15〉∥=sqrt(1+225)=sqrt226

∥vecA+vecB∥-∥vecA∥-∥vecB∥=sqrt226-sqrt82-sqrt40

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