The value of ( a → × b → ) 2 + ( a → · b → ) 2 2 ( a → ) 2 ( b → ) 2 is

Question

The value of ( a → × b → ) 2 + ( a → · b → ) 2 2 ( a → ) 2 ( b → ) 2 is, 0, 1, 1 2, 1 4

MARKS App · Accepted Answer

Given, ( a → × b → ) 2 + ( a → · b → ) 2 2 ( a → ) 2 ( b → ) 2 We know, ( a → ) 2 = a → · a → = a 2 , ( a → × b → ) 2 = a 2 b 2 sin 2 θ , ( a → · b → ) 2 = a 2 b 2 cos 2 θ Where, a → = a , b → = b = a 2 b 2 sin 2 θ + a 2 b 2 cos 2 θ 2 a 2 b 2 = a 2 b 2 ( sin 2 θ + cos 2 θ ) 2 a 2 b 2 = 1 2

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