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Problem

Find the angle between the vectors. (First find a…

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Problem 18 Easy Difficulty

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)

$ a = \langle -1, 3, 4 \rangle , b = \langle 5, 2, 1 \rangle $


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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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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 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
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Problem 22
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Problem 25
Problem 26
Problem 27
Problem 28
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Problem 30
Problem 31
Problem 32
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Problem 36
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Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
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Problem 65

Video Transcript

lesson lesson. We'll finally younger between two vectors A and B. So do this by finding the dot product, and that has given us the magnitude of vector eight times the magnitude of vector B cause Sita, where zika is the angle between two vectors. So here we'll make that cost fee to the subject of the equation So we can divide both sides by the magnitude of the vectors, so that this will cross out that then we have the costs of the angle as a dot be all over the magnitude of a the magnitude of the Okay. So here the cost theater is equal to Yeah, the doctor border took the back test 5 to 1, then the magnitude of them. Uh huh. Oh, so in the dot product, you would multiply the correspondent cams, then you some them some of the correspondent times. Oh, Okay, so here we have one plus nine plus 16. Okay, so that keeps us 26 then. Here we have 25 plus four plus one. That gives us 30. Okay, so the course of the angle, it's negative. Five last six plus five, all of us, the square root of All right. 780. That is 30 times 26. Okay, so we have the cost feature of that is four. So five negative five. Last six gives us one plus four. That gives us what's going on. That gives us five. Oh, so five over square root of 780 Okay, so to get a theater, we take that course or five on the square root of That's Okay. So the articles of 0.1 79 0 to 9, and that is 79 0.686 793 08 to 1 degrees. And this is opposed. Made leaf 80 degrees. Okay, so the angle between the vector A and Vector B supposedly eat the grease. Okay. Thanks for time at the end of the lesson.

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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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