MAT188H1 Midterm: MAT188H1_20169_641483478472mat188tut3sol

• School: UTSG
• Department: Mathematics
• Course: MAT188H1
• Professor: All

Document Summary

Faculty of applied science & engineering, university of toronto. 1 (a) do the lines intersection. x y z. Solution: suppose that the two lines intersect, then there is a point with coordinates (x, y, z) that lies on both lines, i. e. x y z or equivalently, 1 x y z (1) (2) (3) for some s, t r. notice that the above system is satis ed for s = t = 1. Therefore, the point (2, 3, 0) lies on both lines, i. e. the lines intersect. Another way to solve this is to row-reduce the augmented matrix of (2), into: which shows that (2) is always consistent and thus has a unique solution. Find the shortest distance between the two lines and nd the points on the lines that are closest together. Solution: let p (1+s, 1+s, s) and q(2+3t, 1+t, 3) be the points on the lines corresponding to the shortest distance.