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Solution

The given relation is ( a → − b → )×( a → + b → )=2( a → × b → ) .

The distributive property of vector states that,

( a → + b → )( c → + d → )= a → c → + a → d → + b → c → + b → d →

By Distributive property of vector,

( a → − b → )×( a → + b → )= a → a → − b → a → + a → b → − b → b → =0+ a → × b → + a → × b → −0 =2( a → × b → )

Thus, ( a → − b → )×( a → + b → )=2( a → × b → ).

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