Solve Coordinate Geometry Problem: Find Line Equation

[Reshma]

I think my coordinate geometry skills have turned rather rusty.
Just help me out with this problem.

Find the symmetric and parametric equation of a line passing through (3, 4, -1) and parallel to 2i - 3j + 6k.

Here is my attempt at this:

Since the line passes through (3,4,-1) the equation would be given by:
(x - 3) + (y - 4) + (z +1) = 0

But, this looks like the equation of a plane . I am all confused now. How do I relate this line to the vector parallel to it?

 

[HallsofIvy]

Yes, that's the equation of the plane through (3, 4, -1) and perpendicular to 2i- 3j+ 6k. You can't write a line in 3 dimensions in just one equation. Write it in parametric equations:
x= x₀+ at, y= y₀+ bt, z= z₀+ ct where (x₀, y₀, z₀) is a point on the line and ai+ bj+ ck is a vector in the direction of the line.