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SB
Numerade Educator

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Problem 52 Easy Difficulty

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 $

Answer

The two planes are parallel

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Video Transcript

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