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If the perpendicular distance of the point P(0, , 3) from the line x-1 2 = y+1 1 = z 2 is 10 , then the sum of the squares of all possible values of is equal to:

Options

  1. A1
  2. B3
  3. C5
  4. D9

Correct answer

C. 5

Step-by-step solution

Let the given line be L . A point on the line is A(1, -1, 0) and its direction vector is d = 2 i + j + 2 k . The vector joining A to P is AP = (0-1) i + ( - (-1)) j + (3-0) k = - i + ( +1) j + 3 k . The perpendicular distance d of point P from the line is given by d = | AP d | | d | . Now, AP d = vmatrix i & j & k -1 & +1 & 3 2 & 1 & 2 vmatrix = (2 - 1) i + 8 j - (2 + 3) k . The magnitude of the cross product is | AP d | = (2 -1)^2 + 8^2 + (-(2 +3))^2 = 8 ^2 + 8 + 74 . The magnitude of the direction vector is | d |

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