Question

Find a vector equation for the line segment from (2, −3, 8) to (4, 4, 7). (use the parameter t.)

Answer 1

Let  P = (2,-3,8) and Q =(4,4,7)

The parametric equation of a line is given by 
(x,y,z) = t*(xv,yv,zv) + (x0,y0,z0) where 

(xv,yv,zv) is the direction vector PQ which is Q-P => PQ = (4-2, 4-(-3),7-8 ) = (2,7,-1)

And (x0,y0,z0) is any point in the line (for example Q)

So, (x,y,z)  = (2t +4 , 7t +4, -t+7)