Question

已知向量ab满足 | a－b | ＝√6,ab＝1,则 | a＋b | ＝

Answer 1

|a-b|=√(a-b)^2=√(a^2-2ab+b^2)

=√(|a|^2-2ab+|b|^2)

=√6

∴|a|^2-2ab+|b|^2=6

|a|^2+|b|^2=6+2ab

=6+2x1

=8

|a|^2+2ab+|b|^2=8+2ab=8+2x1=10

∴√(a+b)^2=|a+b|=√10