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  1. Find the distance from the point to the plane.
  2. point (0, 2, -1) plane 2x_1 - x_3 = 5
  3.  
  4. Solution:
  5.  
  6. Find ||proj_n AB|| where
  7. ||proj_n AB|| = ||(AB dot n_hat) n_hat||
  8. n_hat = (1/sqrt(5), 0, 2/sqrt(5))
  9. A = (0, 2, -1)
  10. B = (3, 0, 1)
  11. AB = (3, -2, 2)
  12. ||proj_n AB|| = ||[(3, -2, 2) dot (1/sqrt(5), 0, 2/sqrt(5)] n_hat||
  13.               = ||7/sqrt(5) n_hat||
  14.               = ||(7/5, 0, 14/5)||
  15.               = 2sqrt(67)/5
  16.  
  17. Textbook answer: 4/sqrt(5)
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