MATH 101 Lecture 1: 11.5 Lines and Planes in Space
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Math 212 section 11. 5 lines and planes in space. One way of describing the line l is to say that it. Consider the line l through the point p ((cid:1876)(cid:2869),(cid:1877)(cid:2869),(cid:1878)(cid:2869)) and parallel to the vector. The vector is a direction vector for the line l, and a, b, and c consists of all points q (x, y, z) for which the vector (cid:1842)(cid:1843) is parallel to . This means that (cid:1842)(cid:1843) is a scalar multiple of , and you can write (cid:1842)(cid:1843) = t , (cid:1842)(cid:1843) =(cid:1731)(cid:1876) (cid:1876)(cid:2869),(cid:1877) (cid:1877)(cid:2869),(cid:1878) (cid:1878)(cid:2869)(cid:1732)=(cid:1731)(cid:1853),(cid:1854),(cid:1855)(cid:1732)= . By equating corresponding components, you can obtain parametric equations of a line in space. where t is a scalar (a real number). If the direction numbers a, b, and c are all nonzero, you can eliminate the parameter t to obtain symmetric equations of the line. Note: neither parametric equations nor symmetric equations of a line are unique. Example 1: graphing a line using parametric equations.