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# Find a vector equation and parametric equations for the line.The line through the point $(1, 0, 6)$ and perpendicular to the plane $x + 3y + z = 5$

## $\mathbf{r}=(\mathbf{i}+6 \mathbf{k})+t(\mathbf{i}+3 \mathbf{j}+\mathbf{k})$$x=1+t, y=3 t, z=6+t$

Vectors

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##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

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### Video Transcript

So now what we want to do is you want to find the line that passes to the .12 or six. And the spot particular to the line X. That's too white. Plus G equals 2 5. So it's a bit different from what we have done before but it's the same thing. So this is again my this guy and my vector B is just the coefficients of X. Y. And G. So this is one three and one. So the victory question is A. Plus tv. This is 106 nasty Times 1, 3 and one. There's a little equation if you write it in terms of high. So this is I. Plus judo Jessica less six K. Cup. Last two times I cap. That's T. Jacob last cake up. And then for the parametric equation. Yeah With a parametric equation. This is X zero over one. Is why my sorry X -1 Over one equal to 1 -0/3 is equal to G -6/1. And then you get it to A. T. I should do that. Then we just solve it. I was just write it and blow here on the side. So excess D. Plus like one. Why is three D. And G. S. T. Plus six. This is a victory question. That's it.

#### Topics

Vectors

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp