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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 $

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

01:45

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

Vectors

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Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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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.

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