AP EAMCET202120 Aug 2021Evening ShiftMathematicsVector AlgebraActual
The value of ( a → × b → ) 2 + ( a → · b → ) 2 2 ( a → ) 2 ( b → ) 2 is
Options
- A0
- B1
- C1 2
- D1 4
Correct answer
C. 1 2
Step-by-step solution
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