Question

Find the equation of the line passing through the pointsP1( 1, 2, 1) and P2( 2,3,2).

Answer 1

all we need is the direction vector and a point on the line
for the point let's take (1,2,1)
direction vector is < 1,1,1)

vector r = (1,2,1) + t(1,1,1) or change it to whatever form is needed