notes001 (23)

notes001 (23) - ( & 1 ; & 6) and...

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September 2, 2009 NAME____________________________________________ Sketch the curve with vector equation r ( t ) = h 1 + t; 3 t i 2 ± t ± 2 . Indicate with an arrow the direction in which t increases. Solution 1: Note that r ( 2) = 1 ; 6 i and r (2) = h 3 ; 6 i . We also recognize that this curve has parametric equations x = 1 + t , y = 3 t , and is thus a line segment. The line segment, which starts at the point
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Unformatted text preview: ( & 1 ; & 6) and ends at the point (3 ; 6) , is pictured below. Solution 2: Another way to do this is to eliminate the parameter: y = 3 t = 3 ( x & 1) = 3 x & 3 shows that this is the line with slope 3 and y intercept -3 (as pictured above). 1...
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