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Problem 76 Hard Difficulty
Find equations of the planes that are parallel to the plane $ x + 2y - 2z = 1 $ and two units away from it.
Answer
$x+2 y-2 z-7=0, \quad x+2 y-2 z+5=0$
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Top Calculus 3 Educators
Lily A.
Johns Hopkins University
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Campbell University
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Oregon State University
Kristen K.
University of Michigan - Ann Arbor
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Video Transcript
The question they're asking to find the equations of the plane that are parallel to the plane. Express to wipe -2 is equal to one. Yeah. And the two units. Are we drunk this Flynn? So In the question they have given the equation of playing one and We can rearrange this equation in the form that is equal to express to Y -2. Z -1 equal to zero. So in the regular on the equation of a plane is written as Express be bypasses it is equal to zero. So here in the question of the value of A is one. The value of B is too And the value of C is -2. And therefore Here the for the plane one the value of being is -1. So in order to find the distance between the given plane and the plane outs in the question the formula is equal to mhm modular value of D. One minus D. Two divided by route. Under escort. Business courtesy square. So in order to find the equation of the parallel plane. The formula for distance is this. And for the two minding the value of The uh the two we have to put all the values that is you're the one is equal to -1. And the equation for plenty to let it be equal to X plus b. Right to caesar plus the ease equal to zero. And here they will be did too for playing too. And therefore as this Prince a palette and two units come. It's so we can put all the values in the equation to get up Equations of planes. So the is equal to two. And the formula is equal to model the value of the 2-plus 1. Since the one is he going to -1, divided by route under the Value of the normal vector for the plain one scalar form. So this is equal to model the value of the two plus one equal to six from the situation. Therefore, after putting the positive and negative values of the modelers mm belle in the left hand side, we get the two is equal to positive five, four positive modular value. And and we get the two is equal to negative seven for negative Modeler valley. So after finding these two values of being breathe, get the equation of the plane as asking the question that is uh express to y minus 20 for the two positive fi this equation and for the two negative 70 situations. So these are the equations of the plane is asking the question and it's really quite answer
Topics
Vectors
Top Calculus 3 Educators
Lily A.
Johns Hopkins University
Anna Marie V.
Campbell University
Heather Z.
Oregon State University
Kristen K.
University of Michigan - Ann Arbor