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10 cards from this deck
Magnitude and direction
r=a+λb\mathbf{r} = \mathbf{a} + \lambda\mathbf{b}r=a+λb
At point with position vector a\mathbf{a}a
Subtract one position vector from the other
x−a1b1=y−a2b2=z−a3b3\frac{x-a_1}{b_1} = \frac{y-a_2}{b_2} = \frac{z-a_3}{b_3}b1x−a1=b2y−a2=b3z−a3
That coordinate constant; line in a plane
Substitute coords; check same λ\lambdaλ all components
Not parallel and do not intersect
Parallel, intersecting, or skew
Direction vectors parallel AND share common point
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