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Unformatted text preview: MATNYC LAB #8 Intersections and distances 1. Determine whether the lines L 1 and L 2 coincide, are parallel, intersect, or are skew. If they do intersect, find their point of intersection and their angle of intersection. a) L 1 : x = 3+2 t, y = 4 6 t, z = 2+4 t and L 2 : x = 11 t, y = 14+3 t, z = 15 2 t . b) L 1 : x = 4 t, y = 1 + t, z = 3 t and L 2 : x = 2 + 2 t, y = 6 t, z = 3 + 4 t . c) L 1 : x 9 2 = y 5 1 = z 8 3 and L 2 : x 11 2 = y 4 1 = z + 7 3 . 2. a) Show that the line x = 2 + t, y = 1 + 2 t, z = 3 + 4 t lies in the plane 2 x + y z = 2. b) Show that the line x = 1 + t, y = 2 , z = 3 + 5 t intersects the plane x y + z = 5 and find the point of intersection. c) Show that the line x 4 3 = y = z 1 2 is perpendicular to the plane 6 x 2 y + 4 z = 8 and find their point of intersection. 3. Determine if the given planes are parallel and distinct, coincident, or intersect in a line....
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This note was uploaded on 09/26/2011 for the course BIO 293 taught by Professor John during the Spring '11 term at Harvard.
 Spring '11
 JOHN

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