Find the equation of a line going through the points (1,2,3) and (2,1,7)?

Answer 1

p = (1,2,3) + m(1,-1,4) will do, where m is real.

but your teacher probably wants the (1,-1,4) to be a unit vector, so divide it by √18, which is its length: √(1² + (-1)² + 4²).

Answer 2

A Jamaican proverb says:
Given 2 points p1 and p2 the equation is:
(x-x1)/(x2-x1) = (y-y1)/(y2-y1) =(z-z1)/(z2-z1);