Lines and Planes in R3 A line in R3 is determined by a point (a;b;c) on the line and a direction ~v that is parallel(1) to the line The set of points on this line is given by fhx;y;zi= ha;b;ci t~v;t 2Rg This represents that we start at the point (a;b;c) and add all scalar multiples of the vector ~vMar 25, · a, b single values that specify the intercept and slope of the line h the yvalue for the horizontal line v the xvalue for the vertical line For full documentation of the abline() function, check out the R Documentation page How to Add Horizontal Lines The basic code to add a horizontal line to a plot in R is abline(h = some value) Suppose we have the following scatterplot(a) r1(t) = 8 −t,2t,3t (b) r2(t) = t3i −7t3jt3k (c) r3(t) = 8 −4t3,2 5t2,9t3 solution (a) This is a parametrization of the line passing through the point (8,0,0)in the direction parallel to the vector Effect Of Annealing Time And Temperature Parameters On The Microstructure Hardness And Strain Hardening Coefficien
