Parallel lines in 3D, coincident, skew and intersecting lines
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Practice exam-style coincident, parallel, intersecting & skew lines problems
Two vector lines are parallel if their direction vectors are scalar multiples of each other and the lines are not the same.
Consider two lines:
These lines are parallel if b1=kb2 for some scalar k, but a1 does not lie on r2.
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Two vector lines are coincident if they represent exactly the same line, meaning every point on one line also lies on the other. For lines given by:
they are coincident if:
Their direction vectors are parallel, so b1=kb2.
A point from one line (e.g., a2) lies on the other line, satisfying a2=a1+λb1 for some scalar λ.
Two vector lines intersect if they share exactly one common point. That means they are not parallel.
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Two lines in three-dimensional space are skew if they are neither parallel nor intersecting.
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