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Problem

Determine whether the planes are parallel, perpen…
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Urvashi A.
Numerade Educator

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 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 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83

Problem 50 Medium Difficulty

Find the cosine of the angle between the planes $ x + y + z = 0 $ and $ x + 2y + 3z = 1 $

Answer

$\cos \theta=\frac{6}{\sqrt{42}}$

More Answers

01:49

WZ

Wen Z.

Topics

Vectors
Book Cover for Calculus: Early Tra…
Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

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Watch More Solved Questions in Chapter 12

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
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
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
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Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83

Video Transcript

Hello. So the question is straight and from vectors and geometry of space fine. And we have to find a cousin of the angle between the planes. So there are two planes. The funniest X plus Y plus that is equal to zero and the other is X plus two Y plus trees. It is equal to them. And the direction because I know vector corresponding peddler to this plane is I plus J. Plus key is equal. So this is the vector corresponding to let this is victor a corresponding to first plane. And retro be corresponding to second plane is I plus to the G Plus three. Okay so a sign of feta between these two is vector a vector B divided by model vector A and model that will be okay. So it'll be will be I plus G plus k. Don't I place two J last two. Okay divided by magnitude of I plus J plus case square with one plus one plus one. So that will be squared. Okay. Okay so and the magnitude of vector B is one plus four plus. Nice. So like my father solving it we get the value of course of three to is equal to my daughter is one. Jojo is one. Otherwise I dont jay z I don't gaze you so we get one plus two. Last three Divided by Square with three and Square 14. So that will be six or 1 squared what to do. Okay which is the so which is the required value of the sine of the angle between them. So angle will be caused in world six. So we'll spare 42. So its historic wired solution of the equation. Hope this grazers.

Urvashi A.
IIT(BHU), Varanasi

Topics

Vectors
Book Cover for Calculus: Early Tra…
Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes
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In mathematics, a vector (from the Latin word "vehere" meaning &qu…
Video Thumbnail

06:36
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In mathematics, a vector (from the Latin "mover") is a geometric o…
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