MATH 125 Lecture Notes - Lecture 16: Parametric Equation, Dot Product
8 Oct 2015
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Math 125 - lecture 16 - the dot product. Vectors give us a way to visualize a parametric solution. A vector equation can show how a vector will point toward each point on the line. Example: x+2y=3 and 2x+4y =6 are a consistent system in r^3. Parametric solution: {(3-2t, t)| t r} 1 parameter in the shape of a line. Rewrite this set of points as a vector equation. V= = <3-2t,t> = <3,0> + = <3,0>+t <3,0>+t is a vector equation that describes a line. Parametric form: {(p1+tv1, p2+tv2, , pn+tn) | t r} Example: find a vector equation for the line through the points p1=(8,-3) and p2=(5,-5) Direction vector: pick the vector between two points. The direction vectors give u the slope of the line. The lines are parallel when the have same direction vectors and same slopes. These lines are parallel because they are both the same (<2,4>)
