Maths · Equation of a line; Skew lines, the shortest distance between them and its equation

If the points ,(2,0,-1) \) and (4,2,3) lies on a straight line, then what are th

If the points \( (x, y,-3),(2,0,-1) \) and (4,2,3) lies on a straight line, then what are the values of \( x \) and \( y \) respectively?

  • A. 1,-1
  • B. -1,1
  • C. 0,2
  • D. 3,4

Step-by-step solution

For collinearity, vectors between points must be parallel. From points (x,y,-3), (2,0,-1), (4,2,3), vectors are (2-x, -y, 2) and (4-x, 2-y, 6). Equating ratios: (2-x)/(4-x) = (-y)/(2-y) = 2/6 = 1/3. From 2/6=1/3, k=1/3. Then 2-x = (1/3)(4-x) gives x=1; -y = (1/3)(2-y) gives y=-1.
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