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Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one decimal place.)

$ x + 4y - 3z = 1 $ , $ -3x + 6y + 7z = 0 $

Perpendicular or orthogonal

Vectors

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Missouri State University

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University of Michigan - Ann Arbor

Boston College

Mhm. Hello. So the question is taken from victors in the geometry of the space. And the question is to determine whether the planes are parallel, perpendicular or needle. If neither find the angle between them. So given that the planes are Yeah sorry X plus for y minus two. Easy Is equal to so is equal to one. Okay. And other director is minus three. X plus six. Five plus 7 30 0 minus three X plus six. Y plus seven Z is equal to zero. Okay these other two planes we can ride the plane is vector are vector N. Is equal to that constant one. So in this case with the R. Is exciting. Plus by J. Please show you why she plus they decay. Dude I plus 40 minus TK That is equal to one in the similar way. Let us take this as a vector. And so this vector and so if we should write it as vector art or vector Okay vector and one is equal to in this case let us take this as a vector and one. Okay it must be equal to some constant. So victor and one is equal to I. Plus for we'll see minus treaty in the similar way the value of ankle is equal to -3. I if you if you evaluate the director from equation you get and two is equal to minus three. I plus six G Plus 70. These two wild Pegler. Only one then and one. Oh let me tell you that Saleh means that two vectors. The old product of I mean angle between two vectors is called uh zero degree. Okay, so the angle is zero. They go. Even each component of this vector is either equal or the issue of these are equal. Okay, so but this condition it doesn't measure vectors and when is not equal to vector. And and the condition of perpendicular is, the two vectors are perpendicular, only one when and one boat and two is equal to zero. And the parallel when anyone goes and two is equal to zero. These are not backlog. Okay, so let's check the condition of perpendicular. So if we check idolize one, idol J zero, I don't K zero. So from here minus three idolize one. So one dot minus three, 1, 1 into -3 -3 and fall into 60 24 7 into threes 21. So that will be minus 20 which is equal to zero. Okay, so from here we conclude that is too plain south perpendicular to each other. So the angle between these two plane is well perpendicular plane Angle between these two Is equal to nine which is required on some of discussion. Hope this clears