Term	Vectors 	Parametric
Equation 	Polar Equations	
Technical Definition	A quantity having direction as well as magnitude, esp. as determining the position of one point in space relative to another.	•	In mathematics, parametric equations are a method of defining a relation using parameters. A simple kinematical example is when one uses a time parameter to determine the position, velocity, and other information about a body in motion.	In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction.	
Examples	
Problem 1) What is the direction of the vector? Ans:  The direction of the vector is North East or diagonally up and right.
	Find the parametric equations for the line through the points (3,2) and (4,6) so that when t = 0 we are at the point (3,2) and when t = 1 we are at the point (4,6). Ans: (x,y)  =  (1 - t) (3, 2)+ (t) (4, 6)  =  (3 - 3t + 4t, 2 - 2t + 6t)  =  (3 + t, 2 + 4t) x(t)  =  3 + t     and     y(t)  =  2 + 4t	Find a polar equation of the circle with radius |a| centered at (a,0).
Ans: (x − a)2 + y2 = a2 
(rcos() − a)2 + (rsin())2 = a2 
r2cos2() − 2arcos() + a2 + r2sin2() = a2 
r2(cos2() + sin2()) − 2arcos() = 0 Now since cos2() + sin2() = 1, we have: 
r2 − 2arcos() = 0 
r(r − 2acos()) = 0 
r = 0,  r − 2acos() = 0 
	
Summary/Observations	What I learned from vectors is that it’s the direction of anything and magnitude. You use then when you’re trying to figure out the point of something. 	What I learned from parametric equations is a method of defining a relation using parameters. I also learned that a parametric equation can be calculated using the position or velocity.	What I learned from polar equations is that it’s a system of a two dimensional coordinate system. Every point on a plane is determined by a distance from a fixed point and angle.