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A molecule of methane, $ CH_4 $, is structured wi…

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Problem 56 Hard Difficulty

Find the angle between a diagonal of a cube and a diagonal of one of its faces.


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Wen Zheng
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Related Courses

Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Related Topics

Vectors

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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.

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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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Watch More Solved Questions in Chapter 12

Problem 1
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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
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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

Video Transcript

The problem is find the angle between a diagonal of a cube and a diagonal of 1 of its faces. Look at this graph here. So this is the x y d i x y axis and the axis. So this factor is the diagonal this cube here. We assume the last of its edges is equal to 1 point, so the vector of the diagonal of this cube is equal to the use. V is equal to 11 and 1, and a delganal of 1 is basis. This factor this is equal to 10 and 1. Here we denote the angle between these 2 is so we have cosine. Theta is equal to u dot v over magnitude of u times magnitude of v. This is equal to 2 over root of 2 times 3, so this is equal to 2 over root iv. 6 point: this is equal to root of 6 over 3 point, so theta is equal to cosine niverse root to 6 over.

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Video Thumbnail

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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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