## Elementary Geometry for College Students (6th Edition)

$(x,y,z) = (4-n, 1+2n, -3+5n)$
In general we can write an equation for a line in this form: $(x,y,z) = (a,b,c)+n(a',b',c') = (a+a'n, b+b'n,c+c'n)$ where $(a,b,c)$ is a point on the line and $(a',b',c')$ is a direction vector $(4,1,-3)$ is a point on the line $(-1,2,5)$ is a direction vector Note that parallel lines have the same direction vector. We can write an equation for this line: $(x,y,z) = (4,1,-3)+n(-1,2,5) = (4-n, 1+2n, -3+5n)$