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BITSAT2022MathematicsVector AlgebraActual

107. u and v are two non-collinear unit vectors such that | u + v 2 + u v |=1 . Then the value of | u v | is equal to

Options

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

Correct answer

D. | u - v 2 |

Step-by-step solution

Given that, | u + v 2 + u v |=1 array ll & | u + v 2 + u v |^2=1 & 2+2 4 + ^2 =1 & [ u ( u v )= v ( u v )=0] & ^2 2 = 2 & =n 2 , n z & = 2 3 array | u v |= 2 3 = 3 = | u - v 2 |

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