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Find the distance between the given parallel planes.

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

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

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Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

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.

University of Missouri - Columbia

Vectors