Convert the parametric equation x y z 2 1 2 t3 1 2 to nonp

Convert the parametric equation (x, y, z) = (2, -1, -2) + t(3, 1, 2) to nonparametric equation.

Solution

As per the given parametric equation of a line in 3D i.e. (x,y,z) = (2,-1,-2) +t (3,1,2) , we have x = 2 +3t , y = -1+t and z = -2+2t . Then x -2 = 3t so that t = (x -2)/3. Also,   t = (y+1) and 2t = (z+2) so that t = (z+2)/2. Thus, the non-paremetric form of the given equation is (x -2)/3 = (y+1)/1 = (z+2)/2