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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.)

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

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The two planes are parallel

01:20

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

Vectors

Johns Hopkins University

Missouri State University

Campbell University

Oregon 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.

03:21

Determine whether the plan…

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in the question they're asking to determine whether the planes are parallel, perpendicular or neither? If neither find the angle between them. So the two equations of the planes are 19 X -3. Very plus six is equal to two. and second Equation is two x -6. X -4 is equal to zero. Therefore the first condition to take for these two planes is there are parallel or not? Yeah. Yeah. To check equation one and two. Uh Caroline or not. So in order to check whether they are parallel or not, we have to find the ratio between the coefficients of the Coinates of these two planes. Therefore comparing the ratios of the coefficients of X, Y and Z coordinates respectively, It will be equal to -3. Bye two Is equal to nine x -6. Equal to six x -4. Yes. And after simplifying this ratio, we get all the issues to be similar. Therefore this is equal to -3 x 2, 4. All ratios that is four All coordinates. Uh huh. The equations of the do please. Mhm. Since ratios are equal. Yeah. So the two given Okay, mhm planes are Caroline two each other? Yeah. This is the required answer. The given question

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