Problem 1E: Determine whether each statement is true or false in 3. (a) Two lines parallel to a third line are... Problem 2E: Find a vector equation and parametric equations for the line. 2. The line through the point (6, 5,... Problem 3E: Find a vector equation and parametric equations for the line. 3. The line through the point (2, 2.4,... Problem 4E Problem 5E: Find a vector equation and parametric equations for the line. 5. The line through the point (1, 0,... Problem 6E Problem 7E: Find parametric equations and symmetric equations for the line. 7. The line through the points (0,... Problem 8E Problem 9E: Find parametric equations and symmetric equations for the line. 9. The line through the points (8,... Problem 10E: Find parametric equations and symmetric equations for the line. 10. The line through (2, 1, 0) and... Problem 11E: Find parametric equations and symmetric equations for the line. 11. The line through (6, 2, 3) and... Problem 12E: Find parametric equations and symmetric equations for the line. 12. The line of intersection of the... Problem 13E: Is the line through (4, 6, 1) and (2, 0, 3) parallel to the line through (10, 18,4) and (5, 3, 14)? Problem 14E Problem 15E: (a) Find symmetric equations for the line that passes through the point (1, 5, 6) and is parallel to... Problem 16E: (a) Find parametric equations for the line through (2, 4, 6) that is perpendicular to the plane. x ... Problem 17E Problem 18E Problem 19E: Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find... Problem 20E Problem 21E Problem 22E Problem 23E: Find an equation of the plane. 23. The plane through the origin and perpendicular to the vector 1,... Problem 24E Problem 25E: Find an equation of the plane. 25. The plane through the point (1, 12, 3) and with normal vector i +... Problem 26E Problem 27E: Find an equation of the plane. 27. The plane through the point (1, 1, 1) and parallel to the plane... Problem 28E: Find an equation of the plane. 28. The plane through the point (3, 2, 8) and parallel to the plane z... Problem 29E: Find an equation of the plane. 29. The plane through the point (1, 12, 13) and parallel to the plane... Problem 30E Problem 31E: Find an equation of the plane. 31. The plane through the points (0, 1, 1), (1, 0, 1), and (1, 1, 0) Problem 32E: Find an equation of the plane. 32. The plane through the origin and the points (3, 2, 1) and (1, 1,... Problem 33E: Find an equation of the plane. 33. The plane through the points (2, 1, 2), (3, 8, 6), and (2, 3, 1) Problem 34E Problem 35E: Find an equation of the plane. 35. The plane that passes through the point (3, 5, 1) and contains... Problem 36E: Find an equation of the plane. 36. The plane that passes through the point (6, 1, 3) and contains... Problem 37E: Find an equation of the plane. 37. The plane that passes through the point (3, 1, 4) and contains... Problem 38E: Find an equation of the plane. 38. The plane that passes through the points (0, 2, 5) and (1, 3, 1)... Problem 39E Problem 40E Problem 41E: Use intercepts to help sketch the plane. 41. 2x + 5y + z = 10 Problem 42E Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E: Find the point at which the line intersects the given plane. 47. 5x = y/2 = z + 2; 10x 7y + 3z+ 24... Problem 48E: Where does the line through (3, 1, 0) and (1, 5, 6) intersect the plane 2x + y z = 2? Problem 49E: Find direction numbers for the line of intersection of the planes x + y + z = 1 and x + z = 0. Problem 50E Problem 51E Problem 52E: Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle... Problem 53E Problem 54E: Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle... Problem 55E Problem 56E Problem 57E: (a) Find parametric equations for the line of intersection of the planes and (b) find the angle... Problem 58E: (a) Find parametric equations for the line of intersection of the planes and (b) find the angle... Problem 59E Problem 60E: Find symmetric equations for the line of intersection of the planes. z = 2x y 5, z = 4x + 3y 5 Problem 61E Problem 62E: Find an equation for the plane consisting of all points that equidistant from the points (2, 5, 5)... Problem 63E Problem 64E: (a) Find the point at which the given lines intersect: r = 1, 1,0 + t1,1,2 r = 2, 0, 2 + s1, 1, 0... Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E: Find the distance between the given parallel planes. 2x 3y + z = 4, 4x 6y + 2z = 3 Problem 74E: Find the distance between the given parallel planes. 6z = 4y 2x, 9z = 1 3x + 6y Problem 75E: Show that the distance between the parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0... Problem 76E Problem 77E: Show that the lines with symmetric equations x = y = z and x + 1 = y/2 = z/3 are skew, and find the... Problem 78E: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,... Problem 79E: Let L1 be the line through the origin and the point (2, 0, 1). Let L2 be the line through the points... Problem 80E: Let L1 be the line through the points (1, 2, 6) and (2, 4, 8). Let L2 be the line of intersection of... Problem 81E Problem 82E Problem 83E: If a, b, and c are not all 0, show that the equation ax + by + cz + d = 0 represents a plane and a,... format_list_bulleted