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Unformatted text preview: 150) (153 , 129 , 150) feet. 1.3.3. x = (1 , 2 , 2) + t (1 , , 1) . 1.3.5. (a) See the textbook. (b) If p = t a + b = s c + d , then p 1 =t = 2 s3 , p 2 = t + 1 = s + 2 . Adding the equations, 1 = 3 s1 , so s = 2 3 and t = 5 3 . We check that 5 3 a + b = (5 3 , 8 3 ) = 2 3 c + d . 1 (c) If c = (2 ,2) , then c =2 a , so the lines are parallel, and since they do not coincide, they do not intersect. Algebraically, we now get equations p 1 =t = 2 s3 , p 2 = t + 1 =2 s + 2 , adding which produces 1 =1 , which is obviously false for any s, t . 1.3.13. Linearly independent. 1.3.14. Not linearly independent....
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 Spring '08
 Anshelvich
 Math

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