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Find an equation of the plane.

The plane through the point $ (2, 0, 1) $ and perpendicular to the line $ x = 3t, y = 2 - t, z = 3 + 4t $

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$3 x-y+4 z=10$

01:26

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

Vectors

Missouri State University

Baylor University

University of Nottingham

Idaho State University

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 question is taken from Victor's in geometric of the space. And the question is find the equation of plane which passes through 201 and perpendicular to the line. Given that equation of lioness, X. Is equal to treaty, Why is equal to two -T? And that is equal to 3-plus 40. And uh the plane passing to the 0.201. We can try this equation is X over three is equal to the value of two is two minus Y. So that will be by minus two. Over minus one is equal to dead minus 3/4 which is the same. Master. Give an equation of line. We need to find the equation of plane that is perpendicular to this line. Okay so the direction consign and the product of the plane and this direction consigned are equal to zero because both are perpendicular to each other. So the equation of clean passing to 201 and perpendicular to the line one can be how are you Dennis? P x minus two minus one by last four The -1 is equal to you. So that will be T x -6 -6 plus four. That minus four is equal to zero. So that will be three x minus y plus fours. It is equal to 10 which is the required equation of plane passing to the 100.201 and perpendicular to the Cuban life. So hope this clears your doubt

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