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anonymous
 one year ago
Could somebody explain how to do this:
Find the angle between the given vectors to the nearest tenth of a degree.
u = <5, 4>, v = <4, 3>
Answer choices:
A. 9.1 Degrees
B. 1.8 Degrees
C. 0.9 Degrees
D. 11.8 Degrees
Not sure how to find an angle between vectors.
anonymous
 one year ago
Could somebody explain how to do this: Find the angle between the given vectors to the nearest tenth of a degree. u = <5, 4>, v = <4, 3> Answer choices: A. 9.1 Degrees B. 1.8 Degrees C. 0.9 Degrees D. 11.8 Degrees Not sure how to find an angle between vectors.

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anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Do you know how to find the magnitude or length of a vector? And also so you know about scalar or dot product of 2 vectors?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know Scalar and Dot Product. @anikhalder I sort of know magnitude...

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2That's perfect! So let's go through this: What is the length of u vector?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure how to solve for length...

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2so its like, suppose i have a vector a = <3, 4> Then the length of the vector a is : \[\left a \right=\sqrt{3^{2} + {4^{2}}}\] \[\left a \right=\sqrt{25}\] That is the length of vector a is 5 So using the same way can you solve for the length of vector u?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh! Is the magnitude u = SqRt. 41 ?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Perfect! You rock! What about the magnitude (or length) of vector v?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Awesome! Now do you know the formula for dot (or scalar) product of 2 vectors a and b?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, would the product be: a x b = 32 ?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Yes that's correct! But, I will suggest when writing dot product don't use 'x' sign. You will learn that there is another type of product called the vector or cross product which uses this sign...but we don't need to worry about right now. Suppose I have a vector a and vector b Then the dot product of vectors a and b is also defined as: \[a.b=\left a \right\left b \right\cos \theta\] Where theta is the angle between the vectors a and b. So for our question at hand. Let's replace a by u and b by v. So, we get: \[u.v=\left u\right\left v\right\cos \theta\] We can replace u.v as 32 and the magnitudes of u and v on the right hand side of the equation to get: \[\cos \theta=\frac{ u.v }{ \left u \right\left v \right}\] Can you solve for costheta now?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Yes! I find so as well. Now just find the cosine inverse of 0.99 and you'll get it in degrees

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got 8.1 degrees, approximately, but that is not one of my answers.

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2That's what I get and now I must confess that I am confused as well

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2http://onlinemschool.com/math/assistance/vector/angl/ Can you type the values in and see what you get for costheta because I get 0.99 in this website as well

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@anikhalder Can you help me with another problem, and then maybe go back to this one?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Express the complex number in trigonometric form. 3 + 3 square root of three i

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And I'm confused as to what that calculator meant.

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Check this, we were just using 0.99, we cant do that we have to use the full result which was 0.9995120761 plug this and find the cos inverse. You will see that we get our answer :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh. I see. So the answer would be 1.8 degrees?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Yep! And yes just take 4 minutes and see this video on complex numbers! he explains better than me :)))

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Sorry...my bad i forgot to give the link: https://www.youtube.com/watch?v=6z6fzPXUbSQ

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much. (: I watched that video, though, and am still confused on my example. He helped me with a couple others, but the one I posted about is a bit confusing after watching the video.

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2You mean its like : \[3+3\sqrt{3}i\] So, \[\left z \right = \sqrt{3^{2}+(3\sqrt{3})^{2}} = 6\] and \[\tan \theta = \frac{ 3\sqrt{3} }{ 3}\] i.e. \[\theta = 60 degrees\] Now, in polar or trigonometric form, z = \[\left z \right(\cos \theta + i \sin \theta)\] Just substitute the values and find the answer :)))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the Z value?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And is the theta value 120 degrees?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2you can say \[\left z \right\] is like the absolute value of the complex number (like thedw:1437768487456:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the z value is 3SqRt3. But you have in 3 as positive, the 3 is negative. So would that make the equation (in radians): 3SqRt2(Cos2pi/3 + i sin2pi/3)

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2oho...i forgot the minus sign...yep!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, so the theta value is 120 degrees? Not 150?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Wait hold on, how is r coming to 3sqrt3 it should be 6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh. Ok, how do you get 6?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437768935393:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok thanks. So it would be the same answer, but 6 as r vs. 3sqrt3 as r?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2yes it would 6(costheta + i sintheta)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok thanks! Theta = 2pi/3 right?

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2yes. because tantheta in this case is 3sqrt3 / 3 which will give theta as 2pi/3

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2:) I guess so. Please verify the answer with your book and your teacher. If I made any mistake please tell me :)))

anikhalder
 one year ago
Best ResponseYou've already chosen the best response.2Thank you very much for bearing with me! My pleasure! Have a nice night! I will go to sleep!
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