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 $\displaystyle y$.