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MHT CET202618 April 2026Evening ShiftMathematicsVector AlgebraActual

If | a | = | b | = 1, | c | = 2 and a ( a c ) + b = 0 , then the acute angle between a and c is

Options

  1. A2
  2. B3
  3. C4
  4. D6

Correct answer

D. 6

Step-by-step solution

Given a ( a c ) + b = 0 Using the vector triple product expansion: ( a c ) a - ( a a ) c + b = 0 Since | a | = 1 , we have a a = 1 . ( a c ) a - c + b = 0 b = c - ( a c ) a Squaring both sides: | b |^2 = | c |^2 + ( a c )^2| a |^2 - 2( a c )( a c ) Substituting | a | = 1 , | b | = 1 , and | c | = 2 : 1 = 4 + ( a c )^2 - 2( a c )^2 1 = 4 - ( a c )^2 ( a c )^2 = 3 Let be the angle between a and c . Then a c = | a || c | = 2 . (2 )^2 = 3 4 ^2 = 3 ^2 = 3 4 Since is an acute angle, = 3 2 . = 6 Answer: 6

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