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Assignment 2 Multivariate Calculus Math 251 (Fall 2010) A1. Consider the line L in R 2 described parametrically by { r 0 + t v : −∞ < r < ∞} , where r 0 = a x 0 , y 0 A and v = a a, b A . i) Write a formula which gives the distance from the origin to a point on L . Your formula should involve only the constants x 0 , y 0 , a, b and the variable t . ii) Clearly that there is a single value of t which minimizes the distance from the origin to a point on L . Use the Frst derivative test (Section 4.7 of text) to Fnd this optimum value of t (in terms of x 0 , y 0 , a, b ). iii) Substitute your optimum value of t into the distance formula and simplify this as far as possible, to Fnd the minimum distance from the origin to L . iv) Let v be a vector perpendicular to v and write out an expression for comp v r 0 , the scalar projection of r 0 onto v , in terms of the four constants x 0 , y 0 , a, b . v) Explain in your own words why it is not surprising that the answers to parts ii) and
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This note was uploaded on 12/13/2010 for the course MATH 251 taught by Professor Unknown during the Spring '08 term at Simon Fraser.

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251sol2 - Section 12.3 Page 1 Section 12.4 Page 1 Section...

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