NYC-1.L8 - MAT-NYC LAB#8 Intersections and distances 1...

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MAT-NYC 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. If they do intersect in a line, find its symmetric equations. a) 2 x + y - z = 1 and 3 x + 2 y + z = 4. b) x + 2 y + 3 z = 1 and 2 x + 4 y + 6 z = 1. c) 3 x + 6 y + 3 z = 21 and 2 x + 4 y + 2 z = 14.
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