How Do You Formulate the Vector Equation for a Line Given a Point and Direction?

[styxrihocc]

Homework Statement

Find the vector equation of a line that passes through the point (1,3,4) and is parallel to a line that passes through point (5,1,2)

Homework Equations

The Attempt at a Solution

<1,3,4> + t<5,1,2>
<1,3,4> + <5t,t,2t>
<1+5t,3+t,4+2t>

Is my answer correct? if not please point me to the right direction since I'm not quite sure how to solve this problem, thank you.

 

[vela]

Homework Statement

Find the vector equation of a line that passes through the point (1,3,4) and is parallel to a line that passes through point (5,1,2)

Is this the problem exactly as given to you? If so, you can't answer it because there are an infinite number of lines which pass through the point (5, 1, 2).