Mathematics 1229A/B Lecture Notes - Lecture 4: Unit Vector

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

Document Summary

Must be (cid:1874) = c(cid:1873) for some non-zero scalar c. For any vector (cid:1873) and any scalar c: c(cid:1873) = || (cid:1873) . Vector c(cid:1873) is in the same direction as (cid:1873) when c = (cid:2869) . Vector c(cid:1873) is in the opposite direction to (cid:1873) when c = -(cid:2869) . Let (cid:1873) = (2, -3) and (cid:1874) = ((cid:2871)(cid:2872), b) Find the value of b for which (cid:1873) and (cid:1874) are collinear. We need (cid:1874) = c(cid:1873) ((cid:2871)(cid:2872), b) = c(2, -3) So (cid:2871)(cid:2872) = 2c c = (cid:2871)(cid:2876) Find a unit vector in the same direction as (cid:1873) = (1, 2) and a unit vector in the opposite direction to (cid:1874) = (1, -1, 2) (cid:1873) = (1, -2) = (cid:883)(cid:2870)+(cid:884)(cid:2870) = (cid:887) (cid:2869) (cid:2873) (1, 2) = ((cid:2869) (cid:2873),(cid:2870) (cid:2873)) same direction as (cid:1873) . (cid:1874) = (1, -1, 2) = (cid:883)(cid:2870)+(cid:4666) (cid:883)(cid:4667)(cid:2870)+(cid:884)(cid:2870) = (cid:888)