Solving Symmetric Equations to Determine if Points Lie on Line L

[tarheels88]

Homework Statement

My question is how do you use the symmetric equation. For instance I have a question that states: A line L has parametric equations x=4+3t, y=3+4t, z=9-4t. Determine whether or not the points given lie on the line L.
points (17, 14, -9).

Homework Equations

I know that I could set up a symmetric equation like this:
x-4/3= y-3/4= z-9/-4

The Attempt at a Solution

Do I plug in the points and if they are all equaled to one another does it mean they lay on the line L?

 

[ehild]

Homework Equations[/h2]
I know that I could set up a symmetric equation like this:
x-4/3= y-3/4= z-9/-4

Your equations are wrong. x-4/3 = (4-3t)-4/3=4-4/3-3t=8/3-3t, and y-3/4 = (3+4t)-3/4=3-3/4 -4t = 9/4+4t. They are not identical!

If you have addition/subtraction and multiplication/division in a formula, you have to evaluate the multiplication/division first, then the addition/multiplication. You can not spare the parentheses. If there is an expression in parenthesis, evaluate that expression first.

So the correct equations are: t=(x-4)/3=(y-3)/4=(9-z)/4
Now you can plug in the given x,y,z values and see if all equations are true.


ehild