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Problem

Show that the lines with symmetric equations $ x …

11:19

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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.


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Wen Zheng

Related Courses

Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

Related Topics

Vectors

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Top Calculus 3 Educators
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Lectures

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Vectors Intro

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.

Video Thumbnail

11:08

Vector Basics Overview

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.

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Watch More Solved Questions in Chapter 12

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Problem 6
Problem 7
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Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
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Problem 28
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Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
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Problem 39
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Problem 45
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Problem 47
Problem 48
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Problem 50
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Problem 53
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Problem 55
Problem 56
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Problem 64
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Problem 66
Problem 67
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Problem 78
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Problem 81
Problem 82
Problem 83

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

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11:08

Vector Basics Overview

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.

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