Question

Sa se demonstreze urmatoarea inegalitate:

Daca $a_{1}^2+ b_{1}^2+ c_{1}^2=1$ si $a_{2}^2+ b_{2}^2+ c_{2}^2=1$ atunci $( a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2})^2<0$

Answer 1

Asa cum am precizat inainte, folosim inegalitatea Cauchy-Buniakovski-Schwartz:
$( a_{1} a_{2}+ b_{1} b_{2}+ c_{1} c_{2})^{2} \leq ( a_{1}^{2}+ b_{1}^{2}+ c_{1}^{2})( a_{2} ^{2}+ b_{2}^{2}+ c_{2} ^{2}) =1*1=1$.