Finding Line Equation Passing Through Point P0 & Parallel to Line

[lorik]

Homework Statement

The problem is pretty simple but I seem to be missing something essential .Write parametric equation of line which passes through point P0(1,-1,-3) and is parallel with line (x+1)/1=(y+2)/4=(z-1)/0

Homework Equations

solutions are x=2t+1 ,y=4t-1,z=-3

The Attempt at a Solution

I would really really appreciate if u could simply say the magic word because this looks really easy but yet troubling to my brain I think I am tired !

 

[Mark44]

Homework Statement

The problem is pretty simple but I seem to be missing something essential .Write parametric equation of line which passes through point P0(1,-1,-3) and is parallel with line (x+1)/1=(y+2)/4=(z-1)/0

Homework Equations

solutions are x=2t+1 ,y=4t-1,z=-3

The Attempt at a Solution

I would really really appreciate if u could simply say the magic word because this looks really easy but yet troubling to my brain I think I am tired !

If you know a point on a line and a vector parallel to the line, can you get the parametric equations for the line?

You can extract the coordinates of a vector from the symmetric equations (x+1)/1=(y+2)/4=(z-1)/0; namely <1, 4, 0>.

That should get you started.

 

[rock.freak667]

is parallel with line (x+1)/1=(y+2)/4=(z-1)/0

What is the direction of this line?

 

[lorik]

If you know a point on a line and a vector parallel to the line, can you get the parametric equations for the line?

You can extract the coordinates of a vector from the symmetric equations (x+1)/1=(y+2)/4=(z-1)/0; namely <1, 4, 0>.

That should get you started.

And you're Awesome !

 

[HallsofIvy]

In general, any line parallel to
$$\frac{x- x_0}{A}= \frac{y- y_0}{B}= \frac{z- z_0}{C}$$

and passing through the point $(x_0, y_0, z_0)$ is of the form
$$\frac{x-x_1}{A}= \frac{y- y_1}{B}= \frac{z- z_1}{C}$$

That is, it is precisely the numbers A, B, C that determine the direction.