Hi all.

I am stuck at this vector proof question and need help.

Suppose vectors a,b,c satisfy ||a|| > (1/2) + sqrt((1/4)+||c||)

and ||b|| = (||a||)^2

Prove that ||b-c|| > ||a||

Someone please help, thank you.(Worried)(Worried)

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- Aug 30th 2012, 10:48 PMTaTzRE66Vector Proof
Hi all.

I am stuck at this vector proof question and need help.

Suppose vectors a,b,c satisfy ||a|| > (1/2) + sqrt((1/4)+||c||)

and ||b|| = (||a||)^2

Prove that ||b-c|| > ||a||

Someone please help, thank you.(Worried)(Worried) - Aug 31st 2012, 03:08 AMProve ItRe: Vector Proof
You have and .

From the first inequality

I'm afraid I don't know how to continue... - Aug 31st 2012, 10:41 AMawkwardRe: Vector Proof
We have

so (squaring),

hence

substituting ,

But by the triangle inequality,

,

so

Consequently,