Find parametric equations and symmetric equations for the line through $(-6,2,3)$ parallel to the line $\frac12x=\frac13y=z+1$.
Normally I'm given one equation for a line and i put the point and vector with vertices equal to the coefficient of $x,y,z$ but here I have 3 equations so I'm not sure how to proceed. If I plug in the coefficients I'm sure it will be wrong because there's a plus 1 next to $z$, I'm not sure if I'm supposed to convert this from symmetric equation to parallel equation or not. Or maybe it already is a symmetric equation. I checked the book for an example, can't find one, and the online solutions aren't explained very well. if someone could explain how to find these that would help. thank you.
Best Answer
Can you find two points belonging to line $\frac x2=\frac y3=z+1$ ?
$A=(0,0,-1)$ and $B=(2,3,0)$ for instance.
So the line passing through $C=(-6,2,3)$ has equation $M(t)=C+t\,\vec{AB}$