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JEE Main202623 January 2026Evening ShiftMathematicsVector AlgebraActual

Let a , b , c be three vectors such that a b =2( a c ) . If | a |=1,| b |=4,| c |=2 , and the angle between b and c is 60^ , then | a c | is equal to

Options

  1. A1
  2. B2
  3. C0
  4. D4

Correct answer

A. 1

Step-by-step solution

a b = 2( a c ) a ( b - 2 c ) = 0 , so b - 2 c = k a . b c = 4 2 60° = 4 . Dot with c : 4 = 2(4) + k( a c ) k( a c ) = -4 . Dot with a : a b = 2( a c ) + k . Dot with b : 16 = 8 + k a b = 8 + k (- 8 k + k ) = k^2 k = 4 . a c = - 4 k = 1 | a c | = 1 .

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