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# Find parametric equations and symmetric equations for the line.The line through $(-6, 2, 3)$ and parallel to the line $\frac{1}{2} x = \frac{1}{3} y = z + 1$

## $x=-6+2 t, y=2+3 t, z=3+t$ $(x+6) / 2=(y-2) / 3=z-3$

Vectors

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

So what we have to do is now find a christian for the line. That process to the point -62 and three. And Miss Farrell two affects Equals to one x 3. Y. It was to G plus one. Right okay so you start again and this would be deepness work. No this is my age and then we need to find a vector to who is it is apartment garage in. What is the normal vector? So the normal vector here is what is the normal vector two and T. So this would be I made a mistake, there should be a D. Plus This means that this is 23 and one. Yeah. Right so then no solemn this is just a normal veteran. So then the question we started the parliamentary equation our stand is selected. So X Plus 6.2. What we call the Y -3 upon to 33. So if I manage to upon three must be called a G minus three upon one. So this is the equation that we are looking at. And then to find a parametric what I do is I just equated to T. The next is to a -6. Why three T plus two And G. Question T. Last three. That's it. There's nothing else to it.

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Vectors

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp