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.
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You have and . From the first inequality I'm afraid I don't know how to continue...
We have so (squaring), hence substituting , But by the triangle inequality, , so Consequently,
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