Question

向量ab满足|a|=|b|=|a+b|=6,则|a-b|=?

Answer 1

|a+b|²=|a|²+|b|²+2ab

|a-b|²=|a|²+|b|²-2ab

|a-b|²+|a+b|²=2|a|²+2|b|²

|a-b|²=2|a|²+2|b|²-|a+b|²=2*36+2*36-36=3*36

|a-b|=6√3