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AP EAMCET2007MathematicsThree Dimensional Geometry

If a = i - j - k and b =+ i -3 j + k and the orthogonal projection of b on a is 4 3 ( i - j - k ) , then is equal to

Options

  1. A0
  2. B2
  3. C12
  4. D-1

Correct answer

B. 2

Step-by-step solution

Given orthogonal projection of b on a is array r ( b a ) a | a |^2 = 4 3 ( i - j + k ) ( i -3 j + k ) ( i - j - k ) ( i - j - k ) (1+1+1) array = 4 3 ( i - j + k ) aligned & ( +3-1)( i - j - k )=4( i - j + k ) & ( +2)( i - j - k )=4( i - j + k ) aligned On equating the coefficient of i , we get aligned +2 & =4 & =2 aligned

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