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Find a vector equation and parametric equations for the line.

The line through the point $ (2, 2.4, 3.5) $ and parallel to the vector $ 3i + 2j - k $

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$\mathbf{r}=(2 \mathbf{i}+2.4 \mathbf{j}+3.5 \mathbf{k})+t(3 \mathbf{i}+2 \mathbf{j}-\mathbf{k})$$x=2+3 t, y=2.4+2 t, z=3.5-t$

01:49

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

Vectors

Johns Hopkins University

Missouri State University

Baylor University

University of Nottingham

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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03:26

Mhm. All right. We want to. So the following question we want to find a victory question and parameter immigration. From the line back passes to the point two 2.4 and 3.5. And it is parallel to T. I. That's two J -K. This is not the kind of stuff. Yeah. Okay so the parliamentary question is straightforward. So for that what we do is we do expect us to Since it is parallel to three. I kept close to Jacob and these are my victor's, This is my normal doctor. So experience to open three is equal to Y -2.4 of our go Is equal to G -3.5 over-. Like this is this is exactly how you solve it. And that starts the atomic energy question and then just secretly to T. She recorded two P. Then it becomes that access three T plus two why is to T. And I still .4 and jesus- T. for 3.5. This is the parliamentary immigration and then the better equation. It's exactly the same thing. You just passes to whatever passes. That is my A. So these are the form A. Plus some T. B. Where B. Is my normal victory and is the victor that it passes to. So this is to 2.4 3.5 less steep times three two minus. If you want to write it. In terms of I. J. And K. Then it will be to wake up Last 2.4 Jacob Plus 3.5 K. Cup Last three times 3. IPs close to Jacob minus kick. That is how it is.

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