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Find the distance between the given parallel planes.

$ 6z = 4y - 2x , 9z = 1 - 3x + 6y $

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$\frac{1}{3 \sqrt{14}}$

01:43

Wen Zheng

01:17

Carson Merrill

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

Vectors

Johns Hopkins University

Campbell University

University of Nottingham

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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Find the distance between …

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Hello. So it's a good distance. What we need to do is to We arrange this and equipped everything to zero I mean to whatever. Okay so this is equal to zero? Difficult one. And the way you want to make sure is that a coefficient of X. Y. And Z are the same in both equations? Okay So what I've done is to multiply equation one okay. By uh 3/2. So if you do that Question one will now you know be the same. That's a question too. So you can see there the same now. Mhm. So we can use the formula. Okay So d. one and d. two are these values right here? Okay. The A. B. C. Are the coefficients of X, Y. And Z. Respectively? Okay so that's what oh sorry so that's what you see here. So you're so for a subtraction we want the absolute value. So that's gonna be one. Okay then you can now you know so three squared plus negative square plus a nice quiet. Okay so the distance is going to be one of my route 26. Okay thank you very much.

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