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Find the magnitude and direction of each vector. Find the unit vector in the direction of the given vector.$$\mathbf{v}=\langle-3,4\rangle$$

$5, \approx 126.9^{\circ},\left\langle-\frac{3}{5}, \frac{4}{5}\right\rangle$

Precalculus

Algebra

Chapter 5

Applications of Trigonometry and Trigonometric Identities

Section 7

Vectors

Trigonometry

Introduction to Trigonometry

Missouri State University

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University of Michigan - Ann Arbor

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In mathematics, the absolu…

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Magnitude and Direction of…

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Find a unit vector in the …

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Find a vector with the giv…

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Find the vector $\mathbf{v…

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Magnitude of a Vector Find…

okay we're gonna find the magnitude and the direction of our given vector. Now magnitude is always found from squaring each component, adding them together and taking the square root where the angle comes from the inverse tangent of your y. Component over your ex component. So sometimes to draw that makes it the easiest. You can see that the 90 degrees between your X and y. So you see that you're looking for a high pot news and then you can see that the angle is all about tangent because you're given the X and y, you're given the opposite over the adjacent. So let's go ahead and find that magnitude by squaring our sides. When you throw this into your calculator, you might not want to throw a negative in there because if you don't use your apprentices with your square correctly um that could be an issue. But when we do that we get the square root of 25 which is five. And then to find our angle we take that inverse tangent on our calculator of 4/-3. Now what that does is it will give us a um you know a value that's really in quadrant for it actually gave me a negative 53.13 But if you think of where you are that means that you're 53.13 degrees above the X axis. Or you can also consider um adding 182. The value that your calculator gives you will put you in quadrant two. Okay now for a unit vector we just take each of our values. So the negative three comma four and they get divided by the magnitude. And so that creates a high pot news that is just one. And if you wanna square these out some them together and take the square root you will see that you do have your unit vector

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