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What is the angle between the given vector and th…

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Problem 26 Easy Difficulty

Find the vector that has the same direction as $ \langle 6, 2, -3 \rangle $ but has length 4.


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Alan Ghazarians

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Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

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Vectors

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Lectures

Video Thumbnail

02:56

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 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
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Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
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Problem 41
Problem 42
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Problem 48
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Problem 52

Video Transcript

doctor we have here, we wanted to Have the same direction as 6-3. We want to have a length of four or magnitude of form. So first thing we want to do is convert it into a unit vector. So we find the magnitude of this and we see it going to be the square root of six birds. So 36 plus nine Class four, which is going to be seven. So now we get that are vector. Our unit vector Will be won over seven times this right here, if you want, you could always multiply that through. But then we're going to want to multiply this by four. So that way it's no longer a unit factor, but a factor with lengths four. So we see this would be 24/7, 12/7. 8/7. Mhm. Mhm. That's right. Here is going to be our final sector.

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Calculus: Early Transcendentals

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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.

Join Course
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