gaokao 2024 Q5

gaokao · China · beijing 4 marks Vectors Introduction & 2D Vector Properties and Identities (Conceptual)
Given vectors $\boldsymbol { a } , \boldsymbol { b }$, then ``$( \boldsymbol { a } + \boldsymbol { b } ) ( \boldsymbol { a } - \boldsymbol { b } ) = 0$'' is ``$\boldsymbol { a } = \boldsymbol { b }$ or $\boldsymbol { a } = - \boldsymbol { b }$'' a \_\_\_\_ condition.
Necessary but not sufficient
Given vectors $\boldsymbol { a } , \boldsymbol { b }$, then ``$( \boldsymbol { a } + \boldsymbol { b } ) ( \boldsymbol { a } - \boldsymbol { b } ) = 0$'' is ``$\boldsymbol { a } = \boldsymbol { b }$ or $\boldsymbol { a } = - \boldsymbol { b }$'' a \_\_\_\_ condition.