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Find a unit vector that has the same direction as…

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Problem 23 Easy Difficulty

Find a unit vector that has the same direction as the given vector.

$ \langle 6, -2 \rangle $


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Mutahar Mehkri
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Related Courses

Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Related Topics

Vectors

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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

Problem 1
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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

Video Transcript

All right, we've got a question here that asks us to find a unit vector that has the same direction as the Given Victor six to okay. And now the way we can do this is basically we take our vector vector values, and we just divided by the length of the vector. And that's how we can calculate for a unit vector that has the same direction. So what we do is way say, our you vector will be equal to a current vector which we call a over the length of the vector, which is the same thing as our absolute value and student or magnitude. And the way we calculate for that is we take our are to value six and negative, too square. We square them and then add them and put them in the square root. Okay, so six squared plus negative two squared over. Excuse me in the square root. So it becomes 36 plus for, so you get 40. And then the square of 40 comes out to be two, Route 10 and then you take your two values within your vector. And you just divided by two. Route 10. When you do that. You'll get a six over to lieutenant and you get a negative to over to tech. You could simplify this a little bit more. So you get a three on the numerator and lieutenant the denominator, and then you'll get a negative one over route time. Okay, Now, usually, what you don't want is your roots in the denominator. So what we'll do is we'll just multiply the Route 10 on both sides. You'll get a three Route 10 and a 10 in the denominator, and then Route 10 on a turn. We were in the denominator. Okay? And that will be your final answer there for a vector that has the same direction as six. Negative, too. All right, well, I hope that clarifies the question. Thank you so much for watching.

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Calculus: Early Transcendentals

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Video Thumbnail

02:56

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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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