MATH104 Chapter Notes -Parametric Equation

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orchidchinchilla4

7 Oct 2013

School

University of Waterloo

Department

Mathematics

Course

MATH104

Professor

Steve Spencer

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Document Summary

Vector equation of a line in r2 (pages 5-6) The equation x2 = (0. 5)x1 + 1 de nes the x2 component of a point on the line in terms the x1 component. But when we graph the line, we think less of this equation, and more of the following two facts: the x2-intercept is 1 and the slope is 0. 5. In fact, though, we could have used any multiple of up one, right two to nd a second point on the line. So, we can think of the line x2 = (0. 5)x1 + 1 as starting at the point (0, 1), and adding all scalar multiples of the directions up one, right two . Well, if we decide to think of vectors as directions instead of points, then the direction. Up one, right two corresponds to the vector. Then we can turn the (cid:21) (cid:20) 2 (cid:20) x1 (cid:21) 1 (cid:20) 0 (cid:21) (cid:21) (cid:20) 2 (cid:21)

Related Questions

Same line: Different Parametric Equation Every line can be described by infinitely many different sets of parametric equations, since any point on the line and any vector parallel to the line can be used to construct the equations. But how can we tell whether two sets of parametric equations represent the same line? Consider the following two sets of parametric equations:

Line 1:

Line 2:

(a) Find two points that lie on Line 1 by setting and in its parametric equations. Then show that these points also lie on Line 2 by finding two values of the parameter that give these points when substituted into the parametric equations for Line 2.