## anonymous one year ago Let v1 = (2, -6) and v2 = (-4, 7). Compute the unit vectors in the direction of |v1| and |v2|. And can anyone double check if this graph is right? Draw and label v1, v2, and v1+v2. https://gyazo.com/ca330d1301b8dd28e0cdfa3e72f6443c

1. anonymous

2. anonymous

is that all?

3. anonymous

Compute the unit vectors in the direction of |v1| and |v2|. What exactly is this question trying to find?

4. SolomonZelman

$$\large\color{black}{ \displaystyle \frac{\vec{V_1} }{\left|\left| \vec{V_1}\right|\right|} }$$

5. SolomonZelman

This is the unit vector (with magnitude 1) in direction of $$\vec{V_1}$$

6. anonymous

How would you plug in the vector v1 into this equation to find a value?

7. SolomonZelman

Note: V$$_1$$ with two bars on each side, means "magnitude of V$$_1$$.

8. SolomonZelman

You want units vecotrs with the same directions as $$\vec{V_1}$$ and $$\vec{V_2}$$, right?

9. SolomonZelman

|dw:1442448091015:dw|

10. SolomonZelman

that means that if you take each component and divide by this magnitude, you get a unit vector in same direction.

11. SolomonZelman

$$\left|\vec{V_1}\right|=\sqrt{(-2)^2+(6)^2{\color{white}{\large|}}}$$

12. SolomonZelman

I mixed it up, 2, and -6. For magnitude that doesn't matter though. you still get 2√10

13. SolomonZelman

|dw:1442448470003:dw|

14. SolomonZelman

Now, you need to simplify this and you are done with the unit vector for V$$\large _1$$

15. anonymous

Oh, so the value just ends up being the x value of the vector/ magnitude and the y value/magnitude?

16. SolomonZelman

yes

17. SolomonZelman

And same for 3 D vector: < x-component/magnitude, y-component/magnitude, z-component > (and same for any N-dimensional vector (only physics stops at 3 D))

18. SolomonZelman

Then you need to find the magnitude of $$\vec{V_2}$$ and divide each of the $$\vec{V_2}$$'s components by this magnitude. And lets recall that: $$\vec{V_2}=<4,-7>$$

19. SolomonZelman

So the rest is yours:)

20. anonymous

So magnitude of v2 ends up being √65, then the unit vector would be 4/√65 and -7/√65?

21. SolomonZelman

let me see: √{4²+(-7)²}=√{16+49}=√65 Yes, then it would be: < 4/√65 , -7/√65 >

22. SolomonZelman

You can use a taylor polynomial approximation of some nth degree near a=64, of f(x)=√x. (If you want.... :D)

23. SolomonZelman

Imagine you didn't have a calculator, then you would need one ... jk

24. anonymous

Oh jeez, I have no idea about 3d vectors or taylor polynomials at all....But thanks so much for all the help!

25. SolomonZelman

3D is just more complicated to draw, that is all. And tailor polynomial just comes from standard theorem of calculus and integration of parts, starting from: $$\displaystyle \int_{0}^{x}f'(t)dt$$

26. SolomonZelman

You will learn it pretty soon I am sure.... as for now, if you don't have any questions regarding your problem, then good luck:)