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

$ \langle 6, -2 \rangle $

Unit vector is $$\left\langle\frac{3 \sqrt{10}}{10},-\frac{\sqrt{10}}{10}\right\rangle$$

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Oregon State University

Harvey Mudd College

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Idaho State University

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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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