18 02A Problem Set 6 Worked Examples Problem 1 Let F be semi transparent plane containing the points x 1 y 2 and z 3 on the three axes respectively If you put your eye at the point 2 0 0 at what point on F will you see think you see a point of light at 0 1 1 answer 3 Q P 1 2 Let P 2 0 0 and Q 0 1 1 We want the intersection of the line P Q and the plane F Line 2 0 0 t 2 1 1 2 2t t t Plane x y2 z3 1 Intersection 2 2t 2t 3t 1 t 67 pt of intersection 2 7 6 7 6 7 Problem 2 This example will help with pset 7 not pset 6 The hypocycloid is discussed on page 594 595 of the text This is the curve formed by following a point on a circle as it rolls around the inside of another circle Similarly an epicycloid is traced out by a point on a circle rolling around the outside of another circle Assume the fixed circle has radius a and is centered at the origin the rolling circle has radius b the point tracing out the curve is called P the rolling circle starts with its center on the positive x axis with the point P at a 0 Using the hypocycloid as an example give parametric equations for the epicycloid answer Equating arclength along each circle we get a b OC a b cos bi sin bj CP b cos bi sin bj b cos bi sin bj r OP OC CP a b cos b cos bi a b sin b sin bj a b cos b cos 1 a b bi a b sin b sin 1 a b bj x a b cos b cos 1 a b y a b sin b sin 1 a b 18 02A Problem Set 6 Worked Examples y C b P a 0 2 x These plots were made with Matlab using a 1 and various values of b
View Full Document
Unlocking...