# ECOR 1101 Lecture Notes - Lecture 3: Joule, Dot Product, Parallelogram Law

## Document Summary

Cartesian vectors in 3d: 3d vectors are best represented in cartesian vector notation, 3d coordinate system: Fingers curled around z- axis, sweeps from x-axis to y-axis: cartesian unit vectors. Cartesian unit vectors i, j, k designate vectors in the x, y, z directions respectively. The positive directions of the unit vectors are as shown in fig. Cartesian unit vectors will require two successive application of parallelogram law. Direction of cartesian vector: the direction of the. Cartesian vector a is defined by the angles , , and it makes with the x, y, and z axes, respectively. z. Aof cosines directioncoscoscos aaaaaazyx cartesian vector representation: a vector a can be represented using unit vectors as: A = aua, where ua is a unit vector in the direction of a: since the magnitude of a unit vector is 1; Therefore if any two coordinate angles (direction cosines) are known we can find the third.