Are These 3D Lines Parallel? (Full Example!)

Take a look! Are these 3D lines parallel? Can you tell just by looking at their equations? In this video, we will explore a full example of finding out if we have parallel lines in three dimensions by looking at two equations only - no graphs!.

We can show that the lines are parallel by examining their direction vectors and seeing that they are scalar multiples of one another. BUT, this could also make them coincident. To rule this out, we sub in a point on one line into the other, and examine the values of our parameter.

This 3D parallel lines example will help you solve similar problems in the lines and planes unit of the MCV4U vectors course.

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