MAT 1339 Lecture Notes - Lecture 24: Cartesian Coordinate System, Cross Product, Orthogonality

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1339
• Professor: Michael Reeks

Document Summary

Mat1339 - lecture 19 - cartesian third dimension and the cross product. Cartesian third dimension: adding a third dimension to the original (x,y) cartesian plane allows us to evaluate the depth or height (z) of a vector. The coordinates are (x,y,z) and the origin is (0,0,0). These vectors have the same properties as cartesian vectors studied priorly. Cross product: previously we calculated (scalar)(vector) = a vector that as shrunken or grown and (vector)(vector) = a scalar which gives the angle. Now, let"s compute (vector)x(vector) = a vector with the cross product. The cross product detects parallelism unlike the dot product who detects orthogonality. Side-note: no vector is orthogonal to both in this plane. Which means we have to look in the third dimension. Parallel vectors that are tail-to-tail have a direction of 0. In order to be able to curl your finger in the direction of w, you need to turn your hand.