Question

已知向量a,b夹角为45度,且|a|=1,|2a-b|=根号10,则|b|=?

Answer 1

|2a-b|^2

=4|a|^2-4|a||b|cos45+|b|^2

=4|a|^2-2√2|a||b|+|b|^2

=|b|^2-2√2|b|+4

=10

|b|^2-2√2|b|-6=0、(|b|+√2)(|b|-3√2)=0、|b|=3√2.