unicwaan one year ago Can someone help me answer a precalculus question please?

1. unicwaan

Find the angle between the given vectors to the nearest tenth of a degree. u = <2, -4>, v = <3, -8>

2. unicwaan

@EducationsFinest

3. unicwaan

@Vocaloid

4. anikhalder

You can write u as 2i -4j and v as 3i -8j. Then you can apply the dot product rule to find the angle. Take a look at this page: http://www.wikihow.com/Find-the-Angle-Between-Two-Vectors Or take a look at these videos. It will really make your base strong. https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces

5. IrishBoy123

you don't have to re-write them, this is really good compact notation you are using: $$\large \vec u = <2, -4>, \vec v = <3, -8>$$ for $$\large \vec u = <u_x, u_y>, \vec v = <v_x, v_y>$$, we have $$\large \vec u \bullet \vec v = u_x \times v_x + u_y \times v_y = |\vec u||\vec v| cos \theta$$. $$\large \theta$$ is the angle between these vectors. $$\large |\vec u|$$ is the magnitude of $$\large \vec u$$ and equals $$\large \sqrt {u_x^2 + u_y^2}$$, ditto for $$\large |\vec v|$$. that's all you need to answer this, but you should always check first for some trickery in the question, eg where they are clearly parallel.

6. IrishBoy123

@anikhalder thanks for the medal! have one back :p

7. anikhalder

Thank you very much. I really appreciate your explanation and I hope rather than the medals our mutual friend here won't be having troubles finding the angle between vectors anymore :)))

8. IrishBoy123

cool!

9. unicwaan

Thank you all!