MATH 2107 Lecture Notes - Lecture 2: Skew Lines, Horse Length, Cylindrical Coordinate System
11 Oct 2016
School
Department
Course
Professor
Document Summary
Solutions to homework assignment #2, math 253: find the equation of a sphere if one of its diameters has end points (1, 0, 5) and (5, 4, 7). The length of the diameter is p(5 1)2 + ( 4 0)2 + (7 5)2 = 36 = 6, so the radius is 3. The centre is at the midpoint ( 1+5. Hence, the sphere is given as (x 3)2 + (y + 2)2 + (z 6)2 = 9 . 2 , 5+7: find vector, parametric, and symmetric equations of the following lines. (a) the line passing through the points (3, 1, 1. The vector between two points is ~v = h4 3, 3 1, 3 1 the equation of the line is. Vector form: ~r = ~r0 + t~v = h4, 3, 3i + th1, 4, 5. Symmetric from: solving the parametric form for t gives x 4 = y+3. 2i = h4 + t, 3 4t, 3 + 5.
