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JEE Main2004MathematicsThree Dimensional GeometryActual

Let u , v , w be such that | u |=1,| v |=2,| w |=3 . If the projection v along u is equal to that of w along u and v , w are perpendicular to each other then | u - v + w | equals

Options

  1. A2
  2. B7
  3. C14
  4. D14

Correct answer

C. 14

Step-by-step solution

Projection of v along u and w along u is v u | u | and w u | u | respectively According to question v u | u | = w u | u | v u = w u . and v w =0 | u - v + w |^2=| u |^2+| v |^2+| w |^2-2 u v +2 u w -2 v w =14 | u - v + w |= 14

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