# Homework Help: Combining Parametric Equations

1. Jan 9, 2008

### robbondo

1. The problem statement, all variables and given/known data
Show that every point on the line v = (1,-1,2) + t(2,3,1) satisfies the equation
5x - 3y - z - 6 = 0

2. Relevant equations

3. The attempt at a solution

So what I did was solve the equation v by adding the x,z,and z components to get

x = 1 + 2t
y = -1 + 3t
z = 2 + t

So I'm thinking that if I can combine these into one equation that I would end up getting the answer. Problem is I can't figure out how to combine the three equations in an equation with all three variables. I keep getting the function in terms of two variables, or the wrong answer all together. One method I used was solving the z equation for t and then plugging it into the x equation and then the y equation. I tried setting they both equal to zero...

t = z -2
y = 3z-7 y - 3z + 7 = 0
x = 2z-3 x - 2z + 3 = 0

y - 3z + 7 = x -2z + 3

y - z - x + 4 = 0

Obviously this isn't the correct answer. What am I doin' wrong here?

2. Jan 9, 2008

### Dick

Just put your parametric t expressions for x,y and z into 5x-3y-z-6. Do you get zero?

3. Jan 10, 2008

### robbondo

Cool... that works. Why didn't my method work also? Is there more than one equation that can solve that parametric equation?

4. Jan 10, 2008

### Mystic998

Last edited: Jan 10, 2008
5. Jan 10, 2008

### robbondo

Was my algebraic logic correct though? The answer I got was not off by a constant.

6. Jan 10, 2008

### Mystic998

Never mind, I'm an idiot. A line doesn't determine a plane. Wow. Your work is fine, it's just you found a plane that the line is in that isn't the plane you started with.