# Inequality: Proof using Unit Vectors

Prove that (a1b1+a2b2+...+anbn)^2<=(a1^2+a2^2+...+an^2)(b1^2+b2^2+...+bn^2)

where ai, bi are real numbers, i=1,2,...,n

https://brainmass.com/math/algebra/inequality-proof-using-unit-vectors-8596

#### Solution Preview

Proof. Consider two vectors x=(a1,a2,...,an) and y=(b1,b2,...,bn). If all ai's are equal zero or all bi's are equal zero, then x=(0,0,...,0) ...

#### Solution Summary

An inequality is proven using unit vectors. Function vectors are examined.

$2.19