Unformatted text preview: P 1 and P 2 is given by the parametrization 7 −→ p ( t ) = (1 − t ) −→ p 1 + t −→ p 2 with coordinates x = (1 − t ) x 1 + tx 2 y = (1 − t ) y 1 + ty 2 z = (1 − t ) z 1 + tz 2 . The line segment P 1 P 2 consists of the points for which ≤ t ≤ 1 . The value of t gives the portion of P 1 P 2 represented by the segment P 1 −→ p ( t ) ; in particular, the midpoint of P 1 P 2 has position vector 1 2 ( −→ p 1 + −→ p 2 ) = p 1 2 ( x 1 + x 2 ) , 1 2 ( y 1 + y 2 ) , 1 2 ( z 1 + z 2 ) P . 7 This is the parametrized form of the twopoint formula for a line in the plane determined by a pair of points....
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 Fall '08
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 Calculus, Vectors, p1, vector P1 P2, basepoint

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