12. Lines in space





Suppose that the point P_{0} has coordinates x_{0},y_{0},z_{0}, and the nonzero vector v has components a,b,c. Let x,y,z be the coordinates of an arbitrary point P on the line l. Then and the position vectors of P_{0} and P are given by and respectively. The parametric vector equation may be rewritten as that is,
with t R. These equations are called parametric scalar equations of the line.


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