Engineering Calculus Notes 54

Engineering - t y = − 4 2 t(d x = 2 − 4 t y = − 1 − 2 t and x = 1 2 t y = − 4 t 5 Find the points at which the line with parametrization

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42 CHAPTER 1. COORDINATES AND VECTORS (b) The line through the points ( 1 , 2 , 3) and (3 , 2 , 1). (c) The line through the points (2 , 1 , 1) and (2 , 2 , 2). (d) The line through the point (1 , 3 , 2) parallel to the line x = 2 3 t y = 1 + 3 t z = 2 2 t. 4. For each pair of lines in the plane given below, decide whether they are parallel or if not, ±nd their point of intersection. (a) x + y = 3 and 3 x 3 y = 3 (b) 2 x 2 y = 2 and 2 y 2 x = 2 (c) x = 1 + 2 t y = 1 + t and x = 2
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Unformatted text preview: t y = − 4 + 2 t (d) x = 2 − 4 t y = − 1 − 2 t and x = 1 + 2 t y = − 4 + t 5. Find the points at which the line with parametrization −→ p ( t ) = (3 + 2 t, 7 + 8 t, − 2 + t ) that is, x = 3 + 2 t y = 7 + 8 t z = − 2 + t intersects each of the coordinate planes. 6. Determine whether the given lines intersect: (a) x = 3 t + 2 y = t − 1 z = 6 t + 1...
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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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