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# Find parametric equations and symmetric equations for the line.The line through the origin and the point $(4, 3, -1)$

## parametric: $x=4 t, y=3 t z=-t \quad$ symmetric: $\frac{x}{4}=\frac{y}{3}=-z$

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### Video Transcript

So what we're going to do now is find parliamentary situation and symmetry equation for the line That passes through the origin. So 000 and four three and minus one. This is really wonderful. Yeah. Now first we need to fix the vectors so let's fix the origin because I like it and then we need to find the normal vector. And remember here the normal vector B is just the difference between this guy and this guy. So this is 4 0 three minus zero -10. This is for three minus one. So first we find the symmetric equation Which is X -0/4. is why -0/3 Is equal to G zero for -1. And then for the little equation this is just a plus tv So +000 Lasky Times 4. 3 -1. That's it. There's nothing much more work. Okay we want to find the parliamentary equation. But okay so to do that is just we just do the same thing again. So this is if you want to find paramedic then we just quit all this guy to be. I mean I do this on the block just to illustrate that this is another. So you could you to be here one security to be access 40. Why is treaty and G. Is minus T. That's it. So access 40, why is three TGS -T

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