Engineering Calculus Notes 49

Engineering Calculus Notes 49 - 37 1.3 LINES IN SPACE that...

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1.3. LINES IN SPACE 37 —that is, the lines 2 and 3 intersect at the point −→ p 2 (1) = (7 , 4 , 1) = −→ p 3 (2) . Now let us apply the same process to see whether 1 intersects 3 . The vector equation −→ p 1 ( s ) = −→ p 3 ( t ) yields the three coordinate equations 1 3 s = 1 +3 t 2 2 s = 2 + t 3 + s = 3 + t. You can check that these imply, respectively s = t 2 s = 4 + t s = 6 + t. Substituting the frst equality into the other two yields, respectively 2 t = 4 + t t = 6 + t and the only value oF t For which the frst ( resp . second) holds is, respectively, t = 4 t = 3 . Thus our three coordinate equations cannot be satisfed simultaneously; it Follows that
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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.

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