Question

已知|a|= |b|=1,a+b=(-1/5,7/5),求|a-b|的值

Answer 1

|a-b|

=√|a-b|²

=√(a²-2ab+b²)

=√(|a|²-2ab+|b|²)

∵a+b=(-1/5,7/5)

∴|a+b|=√(|a|²+2ab+|b|²)=√2

∴2ab=0

∴|a-b|=√(|a|²-2ab+|b|²)=√(|a|²+|b|²)=√2