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Find an equation of the plane.
The plane through the point $ (1, -1, -1) $ and parallel to the plane $ 5x - y - z = 6 $
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01:14
Wen Zheng
Calculus 3
Chapter 12
Vectors and the Geometry of Space
Section 5
Equations of Lines and Planes
Vectors
Missouri State University
Campbell 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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So the question is taken from victor's and Director of space. And the question is find the equation of plane passing to the point, my one minus one minus one and Pegler to the plane five weeks minus by minus that is equal to six. So the plane passing to the .1 -1 -1 and these spectacular to the plane five x minus y minus Z is equal to six. Okay, so we can write that equation of plain passing to 1 -1 -1 and is feculent to the plane five weeks -8 -8 is equal to six. Can be oh you don't know us five X minus y minus zero plus. Lambda is equal to zero. We can evaluate the value of lambda by substituting the value of X, Y, Z. And x Y Z is one minus one minus one since the plane passing through this point. So that will be five plus one plus one plus lambda is equal to zero. So from here the equation of plane will be by taking λ is equal to -7. So equation of plane will be five weeks minus y minus said Is equal to seven, which is the required equation of the plane. Hope this clears your doubt and thank you
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