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AP EAMCET202419 May 2024Evening ShiftMathematicsVector AlgebraActual

Let a and b be two non-collinear vectors of unit modulus. If u = a -( a b ) b and v = a b , then | v |=

Options

  1. A| u |+| u v |
  2. B| u | 2
  3. C| u |+ | u b | 2
  4. D| u | 5

Correct answer

A. | u |+| u v |

Step-by-step solution

Given, | a |=| b |=1 aligned & Since, u = a -( a b ) b a - b = u & | a |^2+ ^2 | b |^2-2 a b =| u |^2 & | u |^2= ^2 and v = a b | v |= =| u | aligned Now, u v =( a - b ) ( a b )=a ( a b )- b .( a b )=0-0=0 Now, | v |= =| u |+0=| u |+| u v | .

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