# Thread: How do I do parametric and symmetric equations

1. ## How do I do parametric and symmetric equations

Find parametric and symmetric equations of the line passing through
P1 (−3, −2, −1) and P2 (1, 2,3)

Where does the line intersect the x-y plane?

Help!

2. Originally Posted by Quixomatic
Find parametric and symmetric equations of the line passing through
P1 (−3, −2, −1) and P2 (1, 2,3)

Where does the line intersect the x-y plane?

Help!
The direction is $\displaystyle \overrightarrow{P_1 P_2} = <4,4,4>$ so the line is

parametric: $\displaystyle x = 1 + 4t,\; y = 2 + 4t,\; z = 3 + 4t$

symmetric: $\displaystyle \frac{x - 1}{4} = \frac{y - 2}{4} = \frac{z - 3}{4}$

or $\displaystyle x - 1 = y - 2 = z - 3$

Where it intersects the $\displaystyle xy$ plane. Find the $\displaystyle t$ value where $\displaystyle z = 0$. Then use this to find $\displaystyle x$ and $\displaystyle y$.

3. Wow thankyou so much for the quick response, that is extremely helpful So all I do now is set z equal to 0 within its parametric equation and then use that new t value to find x and y?

4. Originally Posted by Quixomatic
Wow thankyou so much for the quick response, that is extremely helpful So all I do now is set z equal to 0 within its parametric equation and then use that new t value to find x and y?
Yep. That's it!