unclear about skew lines not being on same plane

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November 11th 2009, 01:24 PM
superdude

unclear about skew lines not being on same plane

In my text book it says that a two lines are skew iff they are neither parallel or perpendicular to each other (and therefore don't lie on the same plane). The last part confuses me because two lines can be perpendicular or parallel in 2 space but in 3 space the same lines could lie on differnt levels of the z-axis and still be going in the same direction as in 2 space.
November 11th 2009, 01:33 PM
Plato

Quote:

Originally Posted by superdude

In my text book it says that a two lines are skew iff they are neither parallel or perpendicular to each other (and therefore don't lie on the same plane). The last part confuses me because two lines can be perpendicular or parallel in 2 space but in 3 space the same lines could lie on differnt levels of the z-axis and still be going in the same direction as in 2 space.

I certainly hope that no textbook says that.
Two lines are skew to one another if and only if they are non-parallel and non-intersecting.
Therefore, in a plane there are no skew lines.
November 11th 2009, 02:00 PM
superdude

I am starting to see where my confusion lies. This may seem like an unconnected question, but say I was given the parametrization of 2 lines, if I could solve the system of equations for the 2 parameters, does that means that the 2 lines are necessarily perpendicular, or they just intersect?

PS no, you're right, my textbook did not say that explicitly
November 11th 2009, 02:08 PM
Plato

Quote:

Originally Posted by superdude

I am starting to see where my confusion lies. This may seem like an unconnected question, but say I was given the parametrization of 2 lines, if I could solve the system of equations for the 2 parameters, does that means that the 2 lines are necessarily perpendicular, or they just intersect?

You keep using the word perpendicular. I don't think that is what you mean.
In order for two lines to be perpendicular they must intersect and the dot product of their direction vectors must be zero.

If two lines intersect they do not have to be perpendicular.
November 11th 2009, 04:40 PM
hcm2009

Quote:

Originally Posted by Plato

You keep using the word perpendicular. I don't think that is what you mean.
In order for two lines to be perpendicular they must intersect and the dot product of their direction vectors must be zero.

If two lines intersect they do not have to be perpendicular.

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