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JEE MainMathematicsVector Algebra

Let a and b be two vectors such that | a | = 2 and a b = 4 . If c = 2 a + 3 b and | c |^2 = 100 , then | b | is equal to:

Options

  1. A2
  2. B4
  3. C2 7 3
  4. D2 33 3

Correct answer

A. 2

Step-by-step solution

Given | a | = 2 , a b = 4 , and c = 2 a + 3 b . We know that | c |^2 = (2 a + 3 b ) (2 a + 3 b ) | c |^2 = 4| a |^2 + 9| b |^2 + 12( a b ) Substitute the given values into the equation: 100 = 4(2)^2 + 9| b |^2 + 12(4) 100 = 16 + 9| b |^2 + 48 100 = 64 + 9| b |^2 Solving for | b |^2 : 9| b |^2 = 36 | b |^2 = 4 Since magnitude must be non-negative, we get: | b | = 2 Answer: 2

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