Mathematics 1229A/B Lecture Notes - Lecture 14: Hyperplane, Lincoln Near-Earth Asteroid Research

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

Document Summary

P(1, 2, 3, 4) is on the line. = (1, 0, 0, -1) is a direction vector for the line. = (1, 1, 1, 1) is a normal for the hyperplane: = (1, 0, 0, -1, (1, 1, 1, 1) = 1 + 0 + 0 1 = 0. Whether p satisfies w + x + y + z = 5. The line does not lie on the hyperplane. Write a point-parallel form equation for the line l through he point p(1, 0, 2,1) which is perpendicular to the hyperplane (cid:2779)(cid:2778)+(cid:2779)+(cid:2780)=(cid:2782) = (2, -1, 1, 0) is a normal for the hyperplane (use as direction vector) L is perpendicular to the hyperplane (parallel to ) ((cid:1876)(cid:2869),(cid:1876)(cid:2870),(cid:1876)(cid:2871),(cid:1876)(cid:2872)(cid:4667) = (1, 0, 2, 1) + t(2, -1, 1, 0) Find the point of intersection of the line (cid:4666)(cid:4667)=(cid:4666)(cid:2778),(cid:2779),(cid:2780),(cid:2781)(cid:4667)+(cid:4666)(cid:2778),(cid:2777),(cid:2777), (cid:2778)(cid:4667) with the hyperplane 5w 4x 3y + 2 = -10. 3t = -6 t = (cid:2874)(cid:2871) = -2.