1. ## Parametric/Symmetric equations

Find parametric equations and symmetric equations for the line.

The line through (1,-1,1) and parallel to the line x + 2 = (1/2)y = z - 3.

My solution:

(X0, Y0, Z0) = (1,-1,1)
v = (a,b,c) = <1,1/2,1>

x -1 = (y +1)/(1/2) = z -1

x = 1 + t
y = -1 + 1/2t
z = 1 + t

x - 1 = (y + 1) / 2 = z - 1

x = 1 + t
y = -1 + 2t
z = 1 + t

I'm confused where the 2 came from in the y equation.

2. Originally Posted by kenshinofkin
Find parametric equations and symmetric equations for the line.

The line through (1,-1,1) and parallel to the line x + 2 = (1/2)y = z - 3.

My solution:

(X0, Y0, Z0) = (1,-1,1)
v = (a,b,c) = <1,1/2,1>

x -1 = (y +1)/(1/2) = z -1

x = 1 + t
y = -1 + 1/2t
z = 1 + t

x - 1 = (y + 1) / 2 = z - 1

x = 1 + t
y = -1 + 2t
z = 1 + t

I'm confused where the 2 came from in the y equation.
x + 2 = (1/2)y = z - 3:

x + 2 = t => x = t - 2
y/2 = t => y = 2t
z - 3 = t => z = t + 3

So a vector in the direction of this line is (1, 2, 1).

So the required line will have vector equation r = (1, -1, 1) + t(1, 2, 1) and the parametric and symmetric equations follow easily.