Find an equation for the line through point (3, -2, 1) parallel to the line x=1+2t, y=2-t, z=3t

Question

Find parametric equation for the line

Answer 1

Formula for the liine through the point (x0,y0,z0) and parallel to non zero vector <a,b,c> has parametic equations

x = x0+at

y = y0+bt

z = z0+ct

Given line parametic equations are x = 1+2t

y = 2-t

z = 3t

v = <a,b,c> = (2,-1,3)

Required line through the point (3,-2,1) and parallel to the vector v = < 2,-1,3> has parametic equations

x = 3+2t

y = -2-t

z = 1+3t