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

- anonymous

- katieb

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- Alex_Mattucci

Your graph is looking great!

- Alex_Mattucci

is that all?

- anonymous

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

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## More answers

- SolomonZelman

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

- SolomonZelman

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

- anonymous

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

- SolomonZelman

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

- SolomonZelman

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

- SolomonZelman

|dw:1442448091015:dw|

- SolomonZelman

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

- SolomonZelman

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

- SolomonZelman

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

- SolomonZelman

|dw:1442448470003:dw|

- SolomonZelman

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

- anonymous

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

- SolomonZelman

yes

- 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))

- 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: \(\vec{V_2}=<4,-7>\)

- SolomonZelman

So the rest is yours:)

- anonymous

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

- SolomonZelman

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

- SolomonZelman

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

- SolomonZelman

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

- anonymous

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

- 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:
\(\displaystyle \int_{0}^{x}f'(t)dt\)

- 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:)

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