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Find an equation of the plane.

The plane through the point $ (1, \frac{1}{2}, \frac{1}{3}) $ and parallel to the plane $ x + y + z = 0 $

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01:08

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

Vectors

Oregon State University

Harvey Mudd College

Idaho State University

Boston College

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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Hello. So the ocean is taken from vectors and geometry of the space. And uh we have to find the equation of plane which passes to the 0.11 by two and one by three. And paddle to the plain. X plus Y. Plus that is equal to zero. So equation bulls clean passing to 1 1 x two and 1 x three. And yes Caroline. Mhm. To the plane X. Plus Why? Plant that is equal to zero. Can be. Have you done is okay? Yeah. Mhm. Taking X plus Y. Plus zero plus. Lambda is equal to zero. Substituting the value of experience that we get one plus one by two plus one by three is equal to minus of salamander. Celinda will be so that will be 3 to 6. So six plus three plus 2/6 of -10 Lame. That will be equal to minus 11 by six. Substituting this value in equation one we get six X. By taking the calcium of you can see by ghost multiplication plus six five plus six dead is equal to 11. Which is the required equation of plain. They're passing to 11 by 21 by three. And it's no uh pallor to the plane explains why because they're difficult. So hope this clears your doubt and thank you

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