NYC.L7

# NYC.L7 - MAT-NYC LAB #7 Lines and Planes 1. Find both...

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MAT-NYC LAB #7 Lines and Planes 1. Find both symmetric and parametric equations for the line a) through P (2 , - 1 , 3) and perpendicular to the plane 2 x + y = 1. b) through P (1 , 1 , - 1) and perpendicular to both the lines L 1 : x = 2 + t, y = t, z = 1 - 2 t and L 2 : x = 5 + t, y = 5 + 2 t, z = 2 - 3 t . c) lying entirely in the plane x - y + z = 1 and orthogonal to the line [ x, y, z ] = [1 , 1 , 1] + t [ - 1 , 2 , 3] at the point (1 , 1 , 1). 2. Find an equation for the plane a) through P (3 , 0 , - 1) and parallel to 2 x - y + z = 3. b) containing the point (1 , 2 , - 3) and perpendicular to the line x = 1 + t , y = - t , z = - 3 + 2 t . c) through P 1 (1 , 1 , 1), P 2 (2 , - 2 , - 1) and P 3 (0 , 2 , 1). d) with x , y and z -intercepts 2, 3 and 4 respectively. e) containing the lines (ﬁrst check they are coplanar) L 1 : x - 1 1 = z + 9 3 , y = 5 and L 2 : x - 7 3 = y - 5 1 = z - 9 4 . f) containing the point (1 , - 1 , 1) and the y -axis. g) containing the lines

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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.

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NYC.L7 - MAT-NYC LAB #7 Lines and Planes 1. Find both...

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