Determining if a line is perpendicular in ##R^3##

  • Thread starter Calpalned
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  • #1
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Homework Statement


Is the line through (-2, 4, 0) and (1, 1, 1) perpendicular to the line through (2, 3, 4) and (3, -1, -8)?

Homework Equations


R = R0 + tV (for each line)

The Attempt at a Solution


If the lines are parallel, then the V for the two equations will be proportional to each other. How are the two V's related if they are perpendicular?
 

Answers and Replies

  • #2
Dick
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Homework Statement


Is the line through (-2, 4, 0) and (1, 1, 1) perpendicular to the line through (2, 3, 4) and (3, -1, -8)?

Homework Equations


R = R0 + tV (for each line)

The Attempt at a Solution


If the lines are parallel, then the V for the two equations will be proportional to each other. How are the two V's related if they are perpendicular?

Think dot product.
 
  • #3
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I see thank you, Dick.
 
  • #4
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You could also use the cross product if you prefer that.
 
  • #5
LCKurtz
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You could also use the cross product if you prefer that.

And you don't mind doing at least three times as much work...
 
  • #7
SammyS
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You might also want to be sure that the lines intersect and thus are not skew lines.
 

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