In 3-space, 2 lines that are perpendicular to the same aircraft must it is in parallel. However, two lines that space perpendicular to a third line execute not have to be parallel. Explain why. Ns am having actually a very difficult time understanding this problem.

You are watching: Two lines perpendicular to a third line are parallel


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I think this graph will certainly be sufficient to make you know this.look in ~ those planes(instead that lines) perpendicular come the xy plane.they are clearly parallel to each other.

Now look at the x,y and also z axis.look x and also y axis room perpendicular to z axis.but are they parallel?


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Given a line in $3D$ and a allude on it, over there is a plane that passes v that allude and is perpendicular to the line. Currently in a aircraft you deserve to have infinitely many lines, select two which pass v the suggest and lie in the airplane and are NOT perpendicular to every other.

Think about the 3 axes. Two of them space perpendicular to the third one.


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