If $A n d B$ are two vectors and $k$ any scalar quantity greater than zero, then prove that $∣ ∣ A + B ∣ ∣^{2} \leq (1 + k) ∣ ∣ A ∣ ∣^{2} + (1 + \frac{1}{k}) ∣ ∣ B ∣ ∣^{2} ˙$

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A n d B

are two vectors and

k

any scalar quantity greater than zero, then prove that

∣ ∣ A + B ∣ ∣^{2} \leq (1 + k) ∣ ∣ A ∣ ∣^{2} + (1 + \frac{1}{k}) ∣ ∣ B ∣ ∣^{2} ˙

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Question Text

A n d B

are two vectors and

k

any scalar quantity greater than zero, then prove that

∣ ∣ A + B ∣ ∣^{2} \leq (1 + k) ∣ ∣ A ∣ ∣^{2} + (1 + \frac{1}{k}) ∣ ∣ B ∣ ∣^{2} ˙

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