find-the-magnitude-and-direction-of-each-vector-find-the-unit-vector-in-the-direction-of-the-given-v

Question

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

Monica Miller · Accepted Answer

okay we&#x27;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&#x27;re looking for a high pot news and then you can see that the angle is all about tangent because you&#x27;re given the X and y, you&#x27;re given the opposite over the adjacent. So let&#x27;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&#x27;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&#x27;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&#x27;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

Tom Greenwood · Answer

were asked to find the magnitude and direction of Vector V, which is 34 and I&#x27;m just gonna do a quick sketch Vector V here on the X and Y axes. And so 34 would be out to three in the ex direction and up to four on the wind direction. So there&#x27;s Victor V and the reason I want to do the sketches for finding the angle of that. We&#x27;re talking about the angle with the positive X axis. So we&#x27;ve got to make sure we know what Quadrant were in when we were figuring that. So the magnitude of the vector we did a whole lot of these earlier in this section is the square root off your two components squared and add it together. So three squared plus four squared. So that&#x27;s nine plus 16 which is the square root of 25 which is five now, to find out what our angle is, if we just would drop a right angle down here, we have a nice right triangle, and that means are two components. The why and the ex components are making the sides of the right triangle, and we can find out what data is by doing the inverse tangent of the Y component over the X component. So when we do the inverse tangent of 4/3 we end up with an angle of approximately 53 21 degrees.

Griffin Goodwin · Answer

So the question wants us to find the magnitude and the direction of this vector. So we know if we want to take the magnitude of the vector, it&#x27;s going to be equal to the square root of the horizontal component squared plus e vertical component square. So in this case, are horizontal component is three in our vertical component is four. So when we plug this in, we get that the magnitude is equal to the square root of three squared plus for squared, which is equal to the square root of 25 which is also equal to five. So the magnitude of this vector is five. Now, if we want to find the direction of the vector, we know that the horizontal component is equal to three and the vertical component is equal to four. And here&#x27;s the magnitude of the vector. And we&#x27;re trying to find this angle fatal here so we can use trigonometry in this cell for data. So we know that the tangent of data is equal to opposite over adjacent. So if we take the 10 inverse of for over three, that will give us this angle fatal here. And so when we plug this into a calculator, we get that data is equal to 53 0.13 degrees, and that&#x27;s your final answer.

Patrick Burns · Answer

So to get the unit vector for V, first thing we&#x27;re going to do is find the magnitude of the So we&#x27;re going to be taking the square root of each of the component to some of the components squared. So we have three squared, gives us nine we&#x27;re gonna add four squared, which is 16. So we have the square root of nine plus 16 which is 25. That&#x27;s a perfect square. Sweet notes. The magnitude of the is five. Now, we can use this to get our unit vector. So Unit Vector is going to be just like our original vector V, except each of the components are gonna be divided by the magnitude to make it a unit vector. So or three, it&#x27;s gonna become 3/5 in the four is gonna become 4/5 and this is the unit vector for

Ernest Castorena · Answer

the fear of an issue for that goes in the direction of the wrecked a three comma zero. But by instruction we see that it&#x27;s director is just one comma zero along the X axis, the four times that you director is like they&#x27;re really looking for, which is for common zero awesome.

Charles Carter · Answer

Okay, so this problem takes the vector. Um, U equals 34 and it wants us to write a unit vector that goes in the same direction. In order to do that, we just needed to multiply by a scaler value, um, or divide by a scaler value that is equal to the magnitude of this original vector. So the magnitude is equal to the square root of three squared plus four squared, just a square of each term. That&#x27;s gonna give us a spirit of 25 which is five. So our unit vector that has the same, um, direction. Let&#x27;s just represented with a T V with equal 3/5 for over five. Okay, that&#x27;s it. Thank you very much.

Problem

Find the magnitude and direction of each vector. …

Problem 7 Easy Difficulty

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

Answer

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

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

Essentials of Precalculus

Catherine R.

Alayna H.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Richard N. Aufmann, Richard D. NationEssentials of Precalculus

Catherine R.

Alayna H.

Kristen K.

Michael J.

Richard N. Aufmann, Richard D. Nation

Essentials of Precalculus