Question

1. # Find The Angle Between The Given Vectors To The Nearest Tenth Of A Degree. U = <2, -4>, V = <3, -8>

## Introduction

When it comes to solving vector problems, there are a few things you need to keep in mind. One of the most important is the angle between two vectors. This can be tricky to calculate, but with the right approach, it can be relatively straightforward. In this article we will explore how to find the angle between two given vectors and how to do so to the nearest tenth of a degree. We will be using the example of U = <2, -4> and V = <3, -8>. By following our guide, you’ll have your answer in no time!

## The steps to finding the angle between vectors

There are a few steps to finding the angle between vectors:

1. First, you need to find the magnitude of each vector. This can be done by taking the square root of the sum of the squares of each vector’s components.
2. Next, you need to take the dot product of the two vectors. This can be done by multiplying each vector’s corresponding components and then adding them together.
3. Finally, you need to divide the dot product by the product of the magnitudes of the two vectors. This will give you the cosine of the angle between the two vectors, which is what you’re looking for!

## U = <2, -4>, V = <3, -8>

The angle between the given vectors can be found using the following formula:

angle = arccos ( (u•v) / (||u||||v||) )

where u•v is the dot product of vectors u and v, and ||u||||v|| is the product of the norms of vectors u and v.

Plugging in the values for U and V, we get:

angle = arccos( (<2, -4> • <3, -8>) / ( ||<2, -4>||||<3, -8>|| ) )
= arccos( 14 / ( sqrt(20) * sqrt(68) ) ) ~~ 53.13°

## Conclusion

In this article, we provided a step-by-step guide to finding the angle between two given vectors. We began by calculating the dot product and then using that value in conjunction with the magnitudes of each vector to calculate the cosine of the angle in question. Then, using an inverse trigonometric function and our calculator’s degree mode, we were able to find the answer to our problem: The angle between U = <2,-4> and V = <3,-8> is 76.9° when rounded up to the nearest tenth of a degree.

2. Are you stuck trying to find the angle between the given vectors U = <2, -4> and V = <3, -8>? Don’t worry, we got you covered!

The first thing to do is define our vectors. U = <2, -4> and V = <3, -8>. So, U is a 2-dimensional vector with coordinates (2,-4), while V is a 2-dimensional vector with coordinates (3,-8).

The next step is to calculate the dot product of the two vectors. This is done by multiplying each coordinate of U by its corresponding coordinate in V, and then adding up the results. This can be done by hand, or with the help of a calculator.

So, the dot product of U and V is: (2)(3) + (-4)(-8) = 6 + 32 = 38

Now, we can use the dot product to calculate the angle between U and V. This can be done using the formula: θ = arccos(dot product of U and V/ magnitude of U x magnitude of V). So, in our case, θ = arccos(38/sqrt(20)xsqrt(80)) = arccos(38/40) = arccos(0.95) = 54.87°

And that’s it! You’ve now successfully calculated the angle between the given vectors U and V to the nearest tenth of a degree, which is 54.9°.