A line passes through the point (1,-3,5) and is parallel to the vector 2i + 3j + 4k. Find the

A line passes through the point (1,-3,5) and is parallel to the vector 2i + 3j + 4k. Find the standard parametric equations for the line, written using the components of the give vector and the coordinates of the given point.

Parametrize each component separately (x0, y0, z0) and parallel to v1i + v2j + v3k

x = x0 + tv1                  y = y0 + tv2                z = z0 + tv3                        for -infinity < t < infinity

x = 1 + 2t                    y = -3 + 3t                   z = 5 + 4t

Your welcome if you struggled

You didn't explain it, but yeah, that's the right answer.

(1, -3, 5) are your points
<2, 3, 4> are your slopes

So you pair them up:
1 and 2 go together (use for x)
-3 and 3 go together (use for y)
5 and 4 go together (use for z)

And now x = 1 + 2t

etc

(t is just a "dummy variable." You can use any letter, but usually t is used. You plug in for t in all 3 equations to get the x, y, and z values)

You did a better job explaining it. I'm able to search for this question as long as I have the exact numbers or skip the numbers altogether