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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
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

This Question is Closed

Alex_Mattucci
 one year ago
Best ResponseYou've already chosen the best response.0Your graph is looking great!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Compute the unit vectors in the direction of v1 and v2. What exactly is this question trying to find?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \frac{\vec{V_1} }{\left\left \vec{V_1}\right\right} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1This is the unit vector (with magnitude 1) in direction of \(\vec{V_1}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How would you plug in the vector v1 into this equation to find a value?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Note: V\(_1\) with two bars on each side, means "magnitude of V\(_1\).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1You want units vecotrs with the same directions as \(\vec{V_1}\) and \(\vec{V_2}\), right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442448091015:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1that means that if you take each component and divide by this magnitude, you get a unit vector in same direction.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\left\vec{V_1}\right=\sqrt{(2)^2+(6)^2{\color{white}{\large}}}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I mixed it up, 2, and 6. For magnitude that doesn't matter though. you still get 2√10

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442448470003:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Now, you need to simplify this and you are done with the unit vector for V\(\large _1\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, so the value just ends up being the x value of the vector/ magnitude and the y value/magnitude?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And same for 3 D vector: < xcomponent/magnitude, ycomponent/magnitude, zcomponent > (and same for any Ndimensional vector (only physics stops at 3 D))

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Then 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
 one year ago
Best ResponseYou've already chosen the best response.1So the rest is yours:)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So magnitude of v2 ends up being √65, then the unit vector would be 4/√65 and 7/√65?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1let me see: √{4²+(7)²}=√{16+49}=√65 Yes, then it would be: < 4/√65 , 7/√65 >

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1You can use a taylor polynomial approximation of some nth degree near a=64, of f(x)=√x. (If you want.... :D)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Imagine you didn't have a calculator, then you would need one ... jk

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh jeez, I have no idea about 3d vectors or taylor polynomials at all....But thanks so much for all the help!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.13D 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
 one year ago
Best ResponseYou've already chosen the best response.1You 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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