Equality case of Cauchy–Schwarz

If $(a^{2} + b^{2} + c^{2}) (x^{2} + y^{2} + z^{2}) = (a x + b y + cz)^{2}$ , show that $x : a = y : b = z : c$ .

~7 minProof · checked by AICauchy–Schwarzproportionality

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 14

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