Mathematics 1229A/B Lecture Notes - Lecture 6: Parallelogram

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

Document Summary

Vicki olds: cross out the first and last numbers of each row, use a 2 x 2 sequence of numbers using down product up product (left to right) To calculate: with any scalar c. (cid:1873) x (cid:1874) = ((cid:1873)(cid:2870)(cid:1874)(cid:2871) (cid:1873)(cid:2871)(cid:1874)(cid:2870),(cid:1873)(cid:2871)(cid:1874)(cid:2869) (cid:1873)(cid:2869)(cid:1874)(cid:2871),(cid:1873)(cid:2869)(cid:1874)(cid:2870) (cid:1873)(cid:2870)(cid:1874)(cid:2869): write components of (cid:1873) in rows (in order, do the same thing with (cid:1874) under the (cid:1873) components. (cid:1874) x (cid:1873) = -((cid:1873) x (cid:1874) ) = (0 (-3), 3 0, -1 2) Finding the area of a parallelogram or a triangle. (cid:1873) x (cid:1874) gives orthogonal vector to both (cid:1873) and (cid:1874) Find a vector orthogonal to both (cid:1873) = (-1, 1, 2) and (cid:1874) = (3, 2, 0) (cid:1873) x (cid:1874) = (1, 1, 2) x (3, 2, 0) (cid:883) (cid:883) (cid:884) (cid:884) (cid:882) (cid:883) (cid:883) (cid:884) (cid:885) (cid:884) (cid:882) (-4, 6, -5: (-1, 1, 2) = 4 + 6 -10 = 0 (-4, 5, -5, (3, 2, 0) = -12 + 12 0 = 0.