1.3. LINES IN SPACE 41 and so we see that the three lines ℓ A , ℓ B and ℓ C all intersect at the point given by −→ p A p 2 3 P = −→ p B p 2 3 P = −→ p C p 2 3 P = 1 3 −→ a + 1 3 −→ b + 1 3 −→ c . The point given in the last equation is sometimes called the barycenter of the triangle △ ABC . Physically, it represents the center of mass of equal masses placed at the three vertices of the triangle. Note that it can also be regarded as the (vector) arithmetic average of the three position vectors −→ a , −→ b and −→ c . In Exercise 9 , we shall explore this point of view further. Exercises for § 1.3 Practice problems: 1. For each line in the plane described below, give (i) an equation in the form Ax + By + C = 0, (ii) parametric equations, and (iii) a parametric vector equation: (a) The line with slope
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.