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Prove that |vec(a)|-|vec(b)|le |vec(a)-v...

Prove that `|vec(a)|-|vec(b)|le |vec(a)-vec(b)|`.

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(a) What is the geometric significance of the relation |vec(a)+vec(b)|=|vec(a)-vec(b)| ? (b) Prove geometrically that |vec(a)+vec(b)|le |vec(a)|+|vec(b)| .

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Establish the following vector in equalities: (i) |vec(a)-vec(b)| le |vec(a)| +|vec(b)| (ii) |vec(a) -vec(b)| ge |vec(a)| - |vec(b)| What does the equality sign apply ?

For three non-zero vectors vec(a),\vec(b) " and"vec(c ) , prove that [(vec(a)-vec(b))\ \ (vec(b)-vec(c))\ \ (vec(c )-vec(a))]=0