Unformatted text preview: t changes from 0 to 40. 5. ±or instance, the curves r 1 ( t ) = (0 , t ) and r 2 ( t ) = (0 , 1 + t ) are indeed the same straight line. They intersect at inFnitely many points. But the equation r 1 ( t ) = r 2 ( t ) does not have any solution. 6. Since r (0) = (1 , 1 , 0) and r (0) = (1 , , 3), the line tangent to r at (1 , 1 , 0) is the line through (1 , 1 , 0) and is along the direction (1 , , 3). This line has vector representation (1 , 1 , 0) + t (1 , , 3) . 7. Since r 1 (0) = r 2 (1) = (2 , 1 , 3), the curves r 1 and r 2 intersect at (2 , 1 , 3). Now, r 1 (0) = (2 , , 0) r 2 (1) = (1 ,2 , 3) are the directions of the lines tangent to r 1 , r 2 respectively at (2 , 1 , 3). The angle between them is cos1 r (0) · r 2 (1)  r 1 (0)   r 2 (1)  = cos1 1 √ 14 . 1...
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 Spring '11
 ching
 Math, Calculus, Euclidean geometry

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