# Finding the equation of a line through a point and parallel vector

• February 24th 2013, 03:55 PM
bakinbacon
Finding the equation of a line through a point and parallel vector
The question is: Find the equation of a line in R4 through the point (6,2,1,0) and parallel to vector v=<1,2,0,3>.

here's what I have:

(w,x,y,z)=(6,2,1,0)+t<1,2,0,3>
=(6,2,1,0)+<t,2t,0,3t>

are there any further steps to find the equation of the line or is that all I can do?
• February 24th 2013, 04:08 PM
Plato
Re: Finding the equation of a line through a point and parallel vector
Quote:

Originally Posted by bakinbacon
The question is: Find the equation of a line in R4 through the point (6,2,1,0) and parallel to vector v=<1,2,0,3>.
here's what I have:
(w,x,y,z)=(6,2,1,0)+t<1,2,0,3>
=(6,2,1,0)+<t,2t,0,3t>
are there any further steps to find the equation of the line or is that all I can do?

"are there any further steps to find the equation?"

That is purely a matter of opinion.

$\ell (t) = \left\{ {\begin{array}{l} {w(t) = 6 + t} \\ {x(t) = 2 + 2t} \\ {y(t) = 1} \\ {z(t) = 3t} \\ \end{array} } \right.$
• February 24th 2013, 05:58 PM
bakinbacon
Re: Finding the equation of a line through a point and parallel vector
okay, I'll make sure to include that part. thank you