# Math Help - How do I determine a vector of a line..? (more inside)

1. ## How do I determine a vector of a line..? (more inside)

How do I determine a vector equation of a line..?

with the same x-intercept as [x,y,z]=[3,3,0]+t[3,-5,-9] and the same z-intercept as [x,y,z]=[6,-2,-3]+t[3,-1,-2]

Thanks a lot (: !

Hello bebejay

Welcome to Math Help Forum!
Originally Posted by bebejay
How do I determine a vector equation of a line..?

with the same x-intercept as [x,y,z]=[3,3,0]+t[3,-5,-9] and the same z-intercept as [x,y,z]=[6,-2,-3]+t[3,-1,-2]

Thanks a lot (: !
The $z$-intercept on the second line is where it meets the $z$-axis; i.e. $x = y = 0$. This is where $t = -2$: the point whose position vector is $\begin{pmatrix}0\\0\\1\end{pmatrix}$.

But I'm afraid I don't understand what you mean by the $x$-intercept for the first line. This line doesn't intersect the $x$-axis. (When $t=0, z=0, y\ne0$.)

Are you sure you have the correct information here?