PHYSICS 207 Lecture Notes - Lecture 3: Dot Product, Cross Product, Pythagorean Theorem
18 Sep 2016
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Document Summary
A position vector points towards a position in space relative to the origin and has a magnitude and direction. The components of a vector (ax, ay) can be used to calculate the magnitude of the vector: using the pythagorean theorem o. And the magnitude: = tan-1 (ay/ax) Vectors can be added and subtracted through adding and subtracting of two vectors components: a = (ax,ay) and b = (bx,by, a+b = (ax+bx, ay+by, a-b = (ax-bx, ay-by) Position vector addition has the significance of compounding displacements. If a vectors" components are equal to x(t) and y(t) then the vector can be differentiated. This differentiated vector is now the velocity vector v: r = (x(t), y(t)) o. The velocity vector could then be differentiated again to get the acceleration vector o. The dot product generates the angle between two vectors: a b = axbx+ayby. When writing the components we can see how the dot product provides the angle between vectors. o o.
