Mathematics 1229A/B Lecture 10: September 28 Notes

• School: Western University
• Department: Mathematics
• Course: Mathematics 1229A/B
• Professor: Vicki Olds

Document Summary

Vicki olds (direction vector to the line) i. e. 3x = 12 or x = 4. Write a standard form equation of the line with parametric equations x = -1 x = 4 + 0t. P(4, 0) (a point on the line) y = -3t y = 0 + (-3)t = (0, -3) = (0, -3) gives = (3, 0) Standard form equation has form (cid:2869)(cid:1850)+(cid:2870)(cid:1851)= where = . So is 3x+0y = (3, 0: (4, 0) = 12 + 0 = 12. In (cid:2871), the equation ax + by + c = d is the equation of a plane, not a line. In (cid:2871), a vector which is perpendicular to plane is called a normal/normal vector to plane . In (cid:2871) the plane containing point p and with normal vector has point-normal form equation. (cid:4666)(cid:1876) (cid:4667)= 0 i. e. ((cid:2869),(cid:2870),(cid:2871)(cid:4667) (cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667) (cid:4666)(cid:2869),(cid:2870),(cid:2871)(cid:4667)= 0 and standard form equation (cid:2869)(cid:1876)+ (cid:2870)(cid:1877)+(cid:2871)(cid:1878)= where d = normal = (1, -1, 2)