Question

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

Answer 1

The answer is `=-0.025`

Explanation:

`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`