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SB
Numerade Educator

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Problem 55 Medium Difficulty

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

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

Answer

The two planes are parallel

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Video Transcript

in the question they're asking to determine whether planes are parallel, perpendicular or neither. If neither then find the angle between them. The equation of the two planes are number 12 x minus three were equal to set and number 24 X equals three plus six. Why my plus two is it? In order to check all the conditions asking the question. First condition is to check meadow. These planes are Caroline are not so to check this, we have to compare the issues of the coefficients of each other coordinates. So first we have to arrange these two equations. So first equation after arranging is two X-. She by Mine is equal to zero And second equation is four x minus six way minus does it is equal to three in order to compare the coefficients of each other coordinates of these planes And writing them in the form of ratio we get this equal to two x 4 is equal to -3 x -6 is equal to -1x -2. And after simplifying these ratios, the Final ratio is one x 2 is equal to one x 2 is equal to one x 2. Hence mhm Yeah, as all the issues are equal so yeah these planes are parallel to each other and this is the required answer of the given question