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Let be the angle between two unit vectors a and b . If a +2 b is perpendicular to 5 a -4 b , then what is + 2 equal to?

Options

  1. A0
  2. B1 2
  3. C1
  4. D3 +1 2

Correct answer

A. 0

Step-by-step solution

Since, ( a +2 b ) &(5 a -4 b ) are perpendicular vectors. aligned & ( a +2 b ) (5 a -4 b )=0 & 5| a |^2-4 a b +10 a b -8| b |^2=0 & 5 1+6 a b -8=0 Since, | a |=| b |=1 & 6| a || b | =3 & 1 1 = 1 2 = 1 2 aligned So, 2 =2 ^2 -1=2 1 4 -1=- 1 2 Now, + 2 = 1 2 - 1 2 =0

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